Question

4) If x + = = 4, find the value of:
(1) x² + 1/ x²​

Answer 1

Question :

If $x+ \frac{1}{x} = 4$, find the value of :

$(1) x^2 + \frac{1}{x^2}$

Solution :

$\underline{\bold{Given:}}$

• $x+ \frac{1}{x} = 4$

$\underline{\bold{To\:Find:}}$

• The value of :$x^2 + \frac{1}{x^2}$

$\boxed {\pink {{(a + b)}^2 = a^2 +b^2 + 2ab}}$

Squaring on both sides :

$\implies({x + \frac{1}{x} })^{2} = (4)^2 \\\\ \implies x^2 + \frac{1}{x^2} + 2 \times x \times \frac{1}{x} = 16 \\\\ \implies x^2 + \frac{1}{x^2} + 2 = 16 \\\\ \implies x^2 + \frac{1}{x^2} = 16 - 2 \\\\ \implies x^2 + \frac{1}{x^2} = 14$

$\boxed{\green{\therefore {The\:value\:of\:x^2 + \frac{1}{x^2} = 14}}}$

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