Question

The number of real roots of the equation
`sqrt(1+sqrt(5)x+5x^(2))+sqrt(1-sqrt(5)x+5x^(2))=4` is

Answer 1

Correct Answer - C
We have, `sqrt(1+sqrt(5)x+5x^(2))+sqrt(1-sqrt(5)x+5x^(2))=4 " "`………(i)
Also,
`(1+sqrt(5)x+5x^(2))-(1-sqrt(5)x+5x^(2))=2sqrt(5)x " "`........(ii)
Dividing (ii) by (i), we get
`:. sqrt(1+sqrt(5)x+5x^(2))-sqrt(1-sqrt(5)x+5x^(2))=(sqrt(5))/(2)x " "`.......(iii)
Adding (i) and (iii), we get
`sqrt(1+sqrt(5)x+5x^(2))=2+(sqrt(5))/(4)x`
`implies 1+sqrt(5)x+5x^(2)=4+(5)/(16)x^(2)+sqrt(5)x`
`implies x^(2)=(16)/(25) impliesx=+-(4)/(5)`