Question

Full solution answer will be brainlliest​

Answer 1

Answer:

51

Step-by-step explanation:

I hope you understand

Answer 2

$\LARGE\mathfrak{\pink{Solution:-}}$

$\large\mathbb{\orange{GIVEN:-}}$

$x - \frac{1}{x} = 7$

$\large\mathbb{\purple{TO FIND:-}}$

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

$\large\mathbb{\green{FORMULA:-}}$

${(x - \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \cancel{\times x \times \frac{1}{x}} \\ \\ \implies \: {x}^{2} + \frac{1}{ {x}^{2} } - 2$

$\large\mathbb{\red{ACCORDING \:TO\: THE\: QUESTION:-}}$

$x - \frac{1}{x} = 7 \\ \\ \implies{(x - \frac{1}{x} )}^{2} = {7}^{2} - - (Squaring \: both \: sides)\\ \\ \implies {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 49\\ \\ \implies{x}^{2} + \frac{1}{ {x}^{2} } = 49 + 2 \\ \\ \implies{x}^{2} + \frac{1}{ {x}^{2} } = 51$

$\large\mathbb{\purple{ANSWER:-}}$

$\\ \implies \boxed{{x}^{2} + \frac{1}{ {x}^{2} } = 51}$