If x -1- x -7- then find the value of If x-1-x-x2-1-x2A- 51B- 53C- 47D- 49

The correct option is A 51Given: x 1/x= 7, Squaring on both sides, we get (x 1/x)^2 = (7)^2, Using the identity: nbsp; (a b)^2 = a^2 + b^2 2ab, ⇒49=x^ ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identity: (a - b)^2 = a^2 + b^2 - 2ab

If x -1/ x =7...

Question

If $x - \frac{1}{x} = 7,$ then find the value of
$x^{2} + \frac{1}{x^{2}} .$

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Solution

The correct option is B 51
Given: $x - \frac{1}{x} = 7,$
Squaring on both sides, we get
$(x - \frac{1}{x})^{2} = (7)^{2},$
Using the identity:
$(a - b)^{2} = a^{2} + b^{2} - 2 a b,$
$\Rightarrow 49 = x^{2} + \frac{1}{x^{2}} - 2 \times x \times \frac{1}{x}$
$\Rightarrow 49 = x^{2} + \frac{1}{x^{2}} - 2$
$\Rightarrow$ $x^{2} + \frac{1}{x^{2}} = 51$

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If x−1x=7, then find the value of x2+1x2.

The correct option is B 51Given: x−1x=7, Squaring on both sides, we get (x−1x)2=(7)2, Using the identity: (a−b)2=a2+b2−2ab, ⇒49=x2+1x2−2×x×1x ⇒49=x2+1x2−2 ⇒ x2+1x2=51

If $x - \frac{1}{x} = 7,$ then find the value of
$x^{2} + \frac{1}{x^{2}} .$