Question

$x + \frac{1}{x} = 10 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = ?$
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Answer 1

Answer:

$\boxed{\sf\ \implies: {x}^{2} + \frac{1}{ {x}^{2} } = 98 }$

Step-by-step explanation:

$\sf\ \: x + \frac{1}{x} = 10 \\ \\ \sf\ \implies: {(x + \frac{1}{x} })^{2} = {10}^{2} \\ \\ \sf\ \implies: {x}^{2} + 2 \times \cancel{x }\times \frac{1}{ \cancel{x}} + \frac{1}{ {x}^{2} } = 100 \\ \\ \sf\ \implies: {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 100 \\ \\ \sf\ \implies: {x}^{2} + \frac{1}{ {x}^{2} } = 100 - 2 \\ \\ \boxed{\sf\ \implies: {x}^{2} + \frac{1}{ {x}^{2} } = 98 }$

Answer 2

Answer:

x²+1/x²=98

Step-by-step explanation:$\tt\red{ \: x + \frac{1}{x} = 10} \\ \\ \sf\pink{ \implies: {(x + \frac{1}{x} })^{2} = {10}^{2}} \\ \\ \sf\blue{ \implies: {x}^{2} + 2 \times \cancel{x }\times \frac{1}{ \cancel{x}} + \frac{1}{ {x}^{2} } = 100} \\ \\ \sf\green{ \implies: {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 100 }\\ \\ \tt\purple{ \implies: {x}^{2} + \frac{1}{ {x}^{2} } = 100 - 2} \\ \\ \boxed{\tt\ \implies: {x}^{2} + \frac{1}{ {x}^{2} } = 98 }$