Question

$\large\underline{\bf{Question}}$
$\large\red{\sf{if \: x + \frac{1}{x} = 7 \: find \: the \: value \: of \: {x}^{2} + \frac{1}{ {x}^{2} } }}$
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Right answer with explanation​

Answer 1

Step-by-step explanation:

GIVEN:-

X+1/X=7

FIND:-

X²+1/X²=?

SOLUTION:-

X+1/X=7

(X+1/X)²=7²(BECAUSE IF LHS IS SQUARED THEN RHS ALSO SQUARED

X²+1/X²=49

49 IS THE ANSWER

HOPE THIS HELPS YOU DEAR

Answer 2

Answer:

${x}^{2} + \frac{1}{ {x}^{2} } = 47$

Step-by-step explanation:

$x + \frac{1}{x} = 7 \\ {(x + \frac{1}{x}) }^{2} = {(7)}^{2} \\ ( {x}^{2} + \frac{1}{ {x}^{2} } + 2) = 49 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 49 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 47$