Question

if x + 1/x =10 find the value of x² + 1/x²​

Answer 1

Answer:

98 is your answer

Step-by-step explanation:

x+1/x=10

we have to find the value of x²+1/x²

(x+1/x)²=x²+1/x²+2*x*1/x  {(a+b)²=a²+b²+2ab}

=(10)²=x²+1/x²+2

=100=x²+1/x²+2

=100-2=x²+1/x²

98=x²+1/x²

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Answer 2

Answer:

Explanation:

Given :

• x + 1/x = 10

To Find :

• The value of x² + 1/x².

Solution :

$\rm \to \bigg( x + \cfrac{1}{x} \bigg) = 10 \\ \\ \rm [ Squaring \: \: on \: \: both \: \: sides ] \\ \\ \rm \to \: \bigg(x + \cfrac{1}{x} \bigg) {}^{2} = 10 {}^{2} \\ \\ \because \boxed{ \rm \red{(a + b) {}^{2} = a {}^{2} + 2ab + b {}^{2} }} \\ \\ \rm \to \: \bigg(x {}^{2} + 2 \times x \times \cfrac{1}{x} + (\cfrac{1}{x} ) {}^{2} \bigg) = 100 \\ \\ \rm \to \: \bigg(x {}^{2} + 2 \times \not{ x} \times \cfrac{1}{ \not{x}} + (\cfrac{1}{ x} ) {}^{2} \bigg) = 100 \\ \\ \rm \to \: \bigg( x {}^{2} + 2 \times 1 + \cfrac{1 {}^{2} }{x {}^{2} } \bigg) = 100 \\ \\ \rm \to \: \bigg( x {}^{2} + \cfrac{1}{x {}^{2} } \bigg) = 100 - 2 \\ \\ \green{ \rm \to \: \bigg(x {}^{2} + \cfrac{1}{x {}^{2} } \bigg) = 98}$

Hence :

The value of x² + 1/x² is 98.