Question

can't understand pls help

Answer 1

Hi..

answer in attachment :)



#tq

Answer 2

Given that,

$\displaystyle y+\frac{1}{y}=4$

We have to square both the sides.

$\displaystyle \left(y + \frac{1}{y}\right)^2=\ 4^2 \\ \\ \\ (y)^2+\left(2 \times y \times \frac{1}{y}\right)+\left(\frac{1}{y}\right)^2=\ 16 \\ \\ \\ y^2+2+\frac{1}{y^2}=\ 16$

Now subtract 2 from both sides.

$\displaystyle y^2+2+\frac{1}{y^2}-2=\ 16-2 \\ \\ \\ y^2+\frac{1}{y^2}=\Large \textbf{14}$

So, here's the shortcut !!!

$\large \displaystyle \textsf{If\ \ y+\frac{1}{y}=k ,\ \ \ then\ \ y^2+\frac{1}{y^2}=k^2-2 }$

Here, k = 4.

Thus,

$\displaystyle y^2+\frac{1}{y^2}=\ 4^2-2 \\ \\ \\ y^2+\frac{1}{y^2}=\ 16-2 \\ \\ \\ y^2+\frac{1}{y^2}=\ \Large \textbf{14}$