Question

Plsssss help and tell me if the ans is 50/7...plssss

Answer 1

ANSWER IS 14

HOPE THIS HELPS YOU

Answer 2

$x = 2 + \sqrt{3} \: (given) \\ \\ \implies {x}^{2} = {(2 + \sqrt{3)} }^{2} \\ \\ \implies {x}^{2} = 4 + 3 + 4 \sqrt{3} \\ \\ \\ \implies \boxed{ {x}^{2} = 7 + 4 \sqrt{3} } \: \: ....eq.01$

$\frac{1}{ {x}^{2} } = \frac{1}{7 + 4 \sqrt{3} } \\ \\ \\ \implies \frac{1}{ {x}^{2} } = \frac{1(7 - 4 \sqrt{3} )}{7 + 4 \sqrt{3}(7 - 4 \sqrt{3}) } \\ \\ \\ \implies \frac{1}{ {x}^{2} } = \frac{7 - 4 \sqrt{3} }{ {7}^{2} - {(4 \sqrt{3})}^{2}} \\ \\ \\ \implies \frac{1}{ {x}^{2} } = \frac{7 - 4 \sqrt{3} }{49 - 48} \\ \\ \\ \implies \boxed{ \frac{1}{ {x}^{2} } = 7 - 4 \sqrt{3} } \: \: ...(eq.02)$

we have rationalised the denominator above.

Now, we can find the value if the asked questio :-

${x}^{2} + \frac{1}{ {x}^{2} } \\ \\ \\ = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} \: (from \: eq.01 \: and \: 02) \\ \\ \\ = \boxed{14}(ans)$