Question

if (√a+√b)=17 and (√ab)=72 then find the value of √(√a-√b)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The possible values of $\sqrt{(\sqrt{a}-\sqrt{b})}$ are 1,-1, i and -i .

Step-by-step explanation:

Given information: $(\sqrt{a}+\sqrt{b})=17$ and $\sqrt{ab}=72$.

We need to find the value of $\sqrt{(\sqrt{a}-\sqrt{b})}$.

$(\sqrt{a}+\sqrt{b})=17$

Taking square on both sides.

$(\sqrt{a}+\sqrt{b})^2=17^2$

$(\sqrt{a})^2+2\sqrt{a}\sqrt{b}+(\sqrt{b})^2=189$         $[\because (a+b)^2=a^2+2ab+b^2]$

$a+2\sqrt{ab}+b=289$

$a+2(72)+b=289$

$a+b+144=289$

$a+b=289-144$

$a+b=145$                  ..... (1).

$(\sqrt{a}-\sqrt{b})^2=(\sqrt{a})^2-2\sqrt{a}\sqrt{b}+(\sqrt{b})^2$

$(\sqrt{a}-\sqrt{b})^2=a-2\sqrt{ab}+b$

$(\sqrt{a}-\sqrt{b})^2=(a+b)-2(72)$

Using equation (1) we get

$(\sqrt{a}-\sqrt{b})^2=145-144$

$(\sqrt{a}-\sqrt{b})^2=1$

Taking square root on both sides.

$(\sqrt{a}-\sqrt{b})=\pm 1$

$(\sqrt{a}-\sqrt{b})= 1$   and $(\sqrt{a}-\sqrt{b})=-1$

Taking square root.

$\sqrt{(\sqrt{a}-\sqrt{b})}= \pm 1$   and $\sqrt{(\sqrt{a}-\sqrt{b})}=\pm \sqrt{-1}=\pm i$

Therefore, the possible values of $\sqrt{(\sqrt{a}-\sqrt{b})}$ are 1,-1, i and -i .

#Learn more

Find the value of a^3 +b^3 ifa+b=72 ab=5​.

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