Question

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

Answer 1

If
`(1)/(√(a)-√(b))=(1)/(3)` and
`(1)/(√(a)+√(b))=(1)/(2)` then the difference of a and b is 6

SOLUTION:

Given,
`(1)/(√(a)-√(b))=(1)/(3)` →
`√(a)-√(b)=3` ----- (1)

And
`(1)/(√(a)+√(b))=(1)/(2)` →
`√(a)+√(b)=2` --- (2)

We have to find difference of a and b.

Now, add (1) and (2)

`√(a)-√(b)=3`

`√(a)+√(b)=2`

Adding above two equations, we get,

`2 √(a)+0=2+3`

`\begin{array}{l}{2 √(a)=5} \\\\ {√(a)=(5)/(2)} \\\\ {a=(25)/(4)}\end{array}`

substitute
`√(a)` value in (2)

`\begin{array}{l}{(5)/(2)+√(b)=2} \\\\ {√(b)=(2)/(\sin (5)/(2))} \\\\ {√(b)=(4-5)/(2)} \\\\ {√(b)=(-1)/(2)} \\\\ {b=(1)/(4)}\end{array}`

Now, difference of a and b is a – b =
`(25)/(4)-(1)/(4)=(24)/(4)=6`

Hence, the difference of a and b is 6.