Question

If x=7+48 ,find the value of x2+1/x2​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Given : If x=7+\sqrt{48}

To find : The value of \sqrt{x}+\frac{1}{\sqrt{x}} ?

Solution :

x=7+\sqrt{48}

Write it as,

x=7+4\sqrt{3}

x=(2)^2+2\times 2\times \sqrt{3}+(\sqrt{3})^2

x=(2+\sqrt{3})^2

Now taking root both side,

\sqrt{x}=\sqrt{(2+\sqrt{3})^2}

\sqrt{x}=2+\sqrt{3} .....(1)

Now,

\frac{1}{\sqrt{x}}=\frac{1}{2+\sqrt3}

Rationalize the denominator,

\frac{1}{\sqrt{x}}=\frac{1}{2+\sqrt3}\times \frac{2-\sqrt3}{2-\sqrt3}

\frac{1}{\sqrt{x}}=\frac{2-\sqrt3}{2^2-(\sqrt3)^2}

\frac{1}{\sqrt{x}}=\frac{2-\sqrt3}{4-3}

\frac{1}{\sqrt{x}}=2-\sqrt3 ....(2)

Add (1) and (2),

\sqrt{x}+\frac{1}{\sqrt{x}}=2+\sqrt3+2-\sqrt3

\sqrt{x}+\frac{1}{\sqrt{x}}=4

Therefore, the value is \sqrt{x}+\frac{1}{\sqrt{x}}=4

#Learn more

If x=7+root 40 find the value of root x +1/root x