Question

It is a Algebraic equation of class 8 maths​

Answer 1

Answer

• x² + ¹/ₓ² = 18
• x⁴ + ¹/ₓ⁴ = 322

Given

$\bullet \;\; \tt x-\dfrac{1}{x}=4$

To Find

$\tt \bullet \;\; x^2+\dfrac{1}{x^2}\\\\\tt \bullet \;\; x^4+\dfrac{1}{x^4}$

Formula Used

$\bullet \;\; \tt (a-b)^2=a^2+b^2-2ab\\\\\bullet \;\; \tt (a+b)^2=a^2+b^2+2ab$

Solution

a )

Given ,

$\tt (x-\dfrac{1}{x})=4$

Squaring on both sides , we get ,

$\implies \tt (x-\dfrac{1}{x})^2=4^2\\\\\implies \tt x^2+\dfrac{1}{x^2}-2.x.\dfrac{1}{x}=16\\\\\implies \tt x^2+\dfrac{1}{x^2}-2=16\\\\\implies \tt x^2+\dfrac{1}{x^2}=16+2\\\\\implies \underline{\tt x^2+\dfrac{1}{x^2}=18}$

b )

From a ,

$\tt x^2+\dfrac{1}{x^2}=18$

Squaring on both sides , we get ,

$\implies \tt (x^2+\dfrac{1}{x^2})^2=18^2\\\\\implies \tt (x^2)^2+\bigg(\dfrac{1}{x^2}\bigg)^2+2.x^2.\dfrac{1}{x^2}=324\\\\\implies \tt x^4+\dfrac{1}{x^4}+2=324\\\\\implies \tt x^4+\dfrac{1}{x^4}=324-2\\\\\implies \underline{ \tt x^4+\dfrac{1}{x^4}=322}$