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On the following page we have given the solution of Exercise 6.3 of Mathematics 9 (Science) published by Caravan Book House, Lahore. Mathematics 9 (Science) - KPK Solutions of the Textbook of Mathematics for Grade IX, published by The Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan are given here. Forgot account? Solution for 9th Class Math Punjab Text Book Board, Unit 3, Ex 3.4, Question 1 ,part 1&2 According to the syllabus of Punjab Text Book Board, Pakistan 2017. Download Mathcity 9th to BSc solution ,Past Paper apk 9.8 for Android. View Cosine function.pdf from MATH MISC at University of Engineering & Technology. Twitter 4 talking about this. We cover Complete Syllabus of All subjectsOur Study channel MKr. The notes contain all the important questions. Home YouTube Channel There are ten chapters in General Mathematics 9 for Punjab Textbook Board, Lahore. or. 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Class 9 Maths notes according to FBISE syllabus. (iii) $\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36}y^2$, (v) $\frac{4x^6-12x^3y^3+9y^6}{9x^4-24x^2y^2+16y^4},(x \neq 0)$, (vi) $\left( x+\frac{1}{x}\right)^2-4\left( x-\frac{1}{x}\right)$, (vii) $\left( x^2+\frac{1}{x^2}\right)^2-4 \left( x+\frac{1}{x}\right)^2+12,(x \neq 0)$, \begin{align}4x^2-12xy +9y^2\\&=4x^2-6xy-6xy +9y^2\\&= 2x(2x-3y)-3y(2x-3y)\\&= (2x-3y)(2x-3y)\\&= (2x-3y)^2 \end{align}, \begin{align} \sqrt{4x^2-12xy +9y^2}&= \pm (2x-3y) \end{align}, \begin{align}x^2-1+\frac{1}{4x^2}\\&=(x)^2-1+(\frac{1}{2x})^2\\&=(x)^2-2x(\frac{1}{2x})+(\frac{1}{2x})^2\\&= (x-\frac{1}{2x})^2 \end{align}, \begin{align} \sqrt{x^2-1+\frac{1}{4x^2}}&= \pm (x-\frac{1}{2x}) \end{align}, \begin{align}\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36y^2}\\&=(\frac{1}{4}x)^2-\frac{1}{12}xy+ (\frac{1}{6y})^2\\&=(\frac{1}{4}x)^2-2(\frac{1}{4})x(\frac{1}{6y})+ (\frac{1}{6y})^2\\&= (\frac{x}{4}-\frac{1}{6y})^2 \end{align}, \begin{align} \sqrt{\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36}y^2}&= \pm (\frac{x}{4}-\frac{1}{6y}) \end{align}, \begin{align}4(a+b)^2-12(a^2-b^2)+9(a-b)^2\\&=[2(a+b)]^2-2(2)(a+b)(3)(a-b)+[3(a-b)]^2\\&=(2(a+b)-3(a-b))^2\\&= (2a+2b-3a+3b)^2 \\&=(5b-a)^2 \end{align}, \begin{align} \sqrt{4(a+b)^2-12(a^2-b^2)+9(a-b)^2}&= \pm (5b-a) \end{align}, (v) $\frac{4x^6-12x^3y^3+9y^6}{9x^4+24x^2y^2+16y^4},(x \neq 0)$, \begin{align}\frac{4x^6-12x^3y^3+9y^6}{9x^4+24x^2y^2+16y^4}\\&=\frac{(2x^3)^2-2(2x^3)(3y^3)+(3y^3)^2}{(3x^2)^2+2(3x^2)(3y^2)+(4y^2)^2}\\&=\frac{(2x^3-3y^3)^2}{(3x^2+4y^2)^2} \end{align}, \begin{align} \sqrt{\frac{4x^6-12x^3y^3+9y^6}{9x^4+24x^2y^2+16y^4}}&= \pm \frac{(2x^3-3y^3)}{(3x^2+4y^2)} \end{align}, Now \begin{align}\left(x+\frac{1}{x}\right)^2 &=(x-\frac{1}{x})^2+4\\&= a^2+4 \end{align}, \begin{align}\left( x+\frac{1}{x}\right)^2-4\left( x-\frac{1}{x}\right) &=(a^2+4)-4a \\&= a^2-4a+4\\&=(a-2)^2\\&=\left[ (x-\frac{1}{x})-2\right]^2 \end{align}, \begin{align} \sqrt{\left( x+\frac{1}{x}\right)^2-4\left( x-\frac{1}{x}\right)}&= \pm \left[ (x-\frac{1}{x})-2\right]\end{align}, Now \begin{align}\left(x+\frac{1}{x}\right)^2 &=a^2\end{align}, \begin{align}\left(x^2+\frac{1}{x^2}+2\right) &= a^2\end{align}, \begin{align}\left(x^2+\frac{1}{x^2}\right) &= a^2-2\end{align}, \begin{align}\left( x^2+\frac{1}{x^2}\right)^2-4 \left( x+\frac{1}{x}\right)^2+12 &=(a^2-2)^2-4a^2+12 \\&= a^2-4a+4\\&=a^4-4a^2+4-4a^2+12\\&=(a^2)^2-2(a^2)(4)+(4)^2\\&=(a^2-4)^2\end{align}, \begin{align} \sqrt{\left( x^2+\frac{1}{x^2}\right)^2-4 \left( x+\frac{1}{x}\right)^2+12}&= \pm \left[ (a^2-4)\right]\\&= \pm \left[(x+\frac{1}{x})^2-4 \right]\end{align}, \begin{align}(x^2+3x+2)(x^2+4x+3)(x^2+5x+6) &= (x^2+2x+x+2)(x^2+x+3x+3)(x^2+2x+3x+6)\\&= (x(x+2)+1(x+2))(x(x+1)+3(x+1))(x(x+2)+3(x+2))\\&= (x+2)(x+1)(x+1)(x+3)(x+2)(x+3)\\&= (x+2)^2(x+1)^2(x+3)^2\end{align}, \begin{align} \sqrt{(x^2+3x+2)(x^2+4x+3)(x^2+5x+6)}&= \pm (x+2)(x+1)(x+3)\end{align}, \begin{align}(x^2+8x+7)(2x^2-x-3)(2X^2+11x-21)&= (x^2+x+7x+7)(2x^2-3x+2x-3)(2x^2+14x-3x-21)\\&=(x(x+1)+7(x+1))(x(2x-3)+1(2x-3))(2x(x+7)-3(x+7))\\&=(x+1)(x+7)(2x-3)(x+1)(x+7)(2x-3)\\&= (x+1)^2(x+7)^2(2x-3)^2\end{align}, \begin{align} \sqrt{(x^2+8x+7)(2x^2-x-3)(2X^2+11x-21)}&= \pm (x+1)^2(x+7)^2(2x-3)^2\end{align}, Home Class 9 Mathematics Notes - Chapter 9 - Introduction to Coordinate Geometry - Exercise 9.2. 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Create New Account. – Math City These 9th Class Math Notes contain Theory of each and every chapter, Solutions to every exercise and Review exercises in PDF Format. Links You Might Be Interested In: Recent Posts. There are 7 exercise in this chapter. Class 9 Mathematics Notes - Chapter 3 - Logarithms - Exercise 3.2. This Chapter belongs to 9th Class Mathematics book. Class 9 Maths Notes - ( Exercise Solutions PDF ) - Free ILM Algebra is a division of mathematics designed to help solve certain types of problems quicker and easier. Privacy & Cookies Policy More than six years of business experience in digital marketing strategy, business development, sales operation and customer analytics. Create New Account. More than six years of business experience in digital marketing strategy, business development, sales operation and customer analytics. Investimentos - Seu Filho Seguro. Notes of Unit 02 of 9th Class (Science) has been added. 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