Question

If


`a = (2x + √(x) )/(x)`
and

`b = (1 - 2 √(x) )/( √(x) )`
without sing a calculator, show that

`(a + b) {}^(2) = (4)/(x)`
​

Answer 1

Explanation:

Rationalize the denominator of b. So, multiply the numerator and denominator by
`√(x)`

`b = ((1-2√(x)) *√(x))/(√(x)*√(x) )=(1*√(x) -2√(x) *√(x) )/(√(x) *√(x) )\\\\=(√(x) -2x)/(x)\\`

Now, find a +b

`a +b = (2x+√(x) )/(x)+(√(x) -2x)/(x)\\\\=(2x+√(x) +√(x) -2x)/(x)`

Combine like terms

`= (2x-2x+√(x) +√(x) )/(x)\\\\=(2√(x) )/(x)`

Now find (a + b)²

(a +b)² =
`((2√(x) )/(x))^(2)`

`= (2^(2)*(√(x) )^(2))/(x^(2))\\\\= (4* x)/(x^(2))\\\\= (4)/(x)`

Hint:
`√(x) *√(x) =√(x*x)=x`