Question

If x+1÷x=6 find X square+1÷X square
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Answer 1

`\huge\boxed{\sf x^2+(1)/(x^2) = 34 }`

Explanation:

Given:

`\displaystyle x + (1)/(x) = 6`

Using formula:

(a + b)² = a² + 2ab + b² ----------(1)

Here, a = x and b = 1/x

Put in Eq. (1)

`\displaystyle (x + (1)/(x) )^2 = (x)^2+2(x)((1)/(x) )+((1)/(x) )^2\\\\`

Given that,
`\displaystyle x + (1)/(x) = 6`

`\displaystyle So,\\\\(6)^2=x^2+2+(1)/(x^2) \\\\36 = x^2+2+(1)/(x^2)`

• Subtract 2 from both sides

`\displaystyle 36 - 2 = x^2+(1)/(x^2) \\\\34 = x^2+(1)/(x^2) \\\\x^2+(1)/(x^2) = 34 \\\\\rule[225]{225}{2}`