Question

if x=3+√5/2.then find the value of x square+1/x square​

Answer 1

Answer:

           7

Step-by-step explanation:

$\displaystyle x=\frac{3+\sqrt5}2\\\\\Rightarrow\frac1x=\frac2{3+\sqrt5}=\frac{2(3-\sqrt5)}{(3+\sqrt5)(3-\sqrt5)}=\frac{2(3-\sqrt5)}{9-5}=\frac{3-\sqrt5}2$

So...

$\displaystyle x+\frac1x=\frac{3+\sqrt5}2+\frac{3-\sqrt5}2=3$

and therefore...

$\displaystyle x^2+\frac1{x^2}=\left(x+\frac1x\right)^2-2=3^2-2=7$

Answer 2

Answer:

If x= 2, then the value of x square +3×+5