Question

If 1 /√−√ = 1/3 and 1/√+√ = 1/2 ,then find the difference of a and b

Answer 1

√a - √b = 3

√a + √b = 2

Multiply these both

(√a - √b)(√a + √b) = 3(2)

(√a)² - (√b)² = 6 {(a+b)(a-b)=a²-b²}

a - b = 6

Hence the difference between a and b is 6.

Hope it helps!!! :)

Answer 2

❣️$\textbf{\large{\blue{\underline{Step by step Explanation:-}}}}$

$\mathtt{\frac{1}{\sqrt{a}-\sqrt{b}}=\frac{1}{3}}$

$\mathtt{\implies{\sqrt{a}-\sqrt{b}=3}}$___(1)

$\mathtt{\frac{1}{\sqrt{a}+\sqrt{b}}=\frac{1}{2}}$

$\mathtt{\implies{\sqrt{a}+\sqrt{b}=2}}$___(2)

$\textit{\underline{from (1),,}}$

$\mathtt{\sqrt{a}-\sqrt{b}=3}$

$\mathtt{\implies{\sqrt{a}=3+\sqrt{b}}}$___(3)

$\mathit{\underline{from(3),,the,,value,,of \sqrt{a},, putting,,in,,(2)}}$

$\textit{\underline{Hence,,}}$

$\mathtt{\sqrt{a}+\sqrt{b}=2}$

$\mathtt{\implies{3+\sqrt{b}+\sqrt{b}=2}}$

$\mathtt{\implies{2\sqrt{b}=2-3}}$

$\mathtt{\implies{\sqrt{b}=\frac{-1}{2}}}$

$\mathtt{\implies{b=(\frac{-1}{2})^{2}}}$

$\mathtt{\implies{b=\frac{1}{4}}}$

$\textit{\underline{Since,,}}$

$\textit{The value of,,b,,putting on (1)}$

$\mathtt{\sqrt{a}-\sqrt{b}=3}$

$\mathtt{\implies{\sqrt{a}-\sqrt{\frac{1}{4}}=3}}$

$\mathtt{\implies{\sqrt{a}-\frac{1}{2}=3}}$

$\mathtt{\implies{\sqrt{a}=3+\frac{1}{2}}}$

$\mathtt{\implies{\sqrt{a}=\frac{6+1}{2}}}$

$\mathtt{\implies{\sqrt{a}=\frac{7}{2}}}$

$\mathtt{\implies{a=(\frac{7}{2})^{2}}}$

$\mathtt{\implies{a=\frac{49}{4}}}$

$\textit{\underline{Since,, the difference of a and b=}}$

$\mathtt{a-b=\frac{1}{4}-\frac{49}{4}}$

$\mathtt{=\frac{1-49}{4}}$

$\mathtt{=\frac{-48}{4}}$

$\mathtt{=-12}$

$\textit{\underline{Hence,,}}$

$\textit{The value of 'a'}$

$\mathtt{\implies{\boxed{\pink{\frac{1}{4}}}}}$

$\textit{The value of 'b'}$

$\mathtt{\implies{\boxed{\pink{\frac{49}{4}}}}}$

$\textit{and, the difference of 'a' and 'b'}$

$\mathtt{\implies{\boxed{\pink{-12}}}}$

❣️$\textbf{\small{\red{Hope you like it}}}$❣️

$\textit{\small{\green{please mark it as Brainliest answer.. thanks}}}$