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(7) Given that
y is a positive integer and
y-(1)/(y)=6, find the value of
y^(2)+(1)/(y^(2)).

( $7$ ) Given that $y$ is a positive integer and $y-\frac{1}{y}=6$ , find the value of $y^{2}+\frac{1}{y^{2}}$ .

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Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. (

7

) Given that

y

is a positive integer and

y-\frac{1}{y}=6

, find the value of

y^{2}+\frac{1}{y^{2}}

.

Isolate $y^2 + \frac{1}{y^2}$ : Now, we need to isolate $y^2 + \frac{1}{y^2}$ by adding $2$ to both sides of the equation. $\newline$ $y^2 + \frac{1}{y^2} - 2 + 2 = 36 + 2$ $\newline$ $y^2 + \frac{1}{y^2} = 38$
Add $2$ to both sides: We've found the value of $y^2 + \frac{1}{y^2}$ .

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