Select whether the equation has a solution or not. √ √(x + 1) = 7 - 2 √(x) x+ 1 = 7 - 2√2 roots​

Question

Select whether the equation has a solution or not.

√

`√(x + 1) = 7 - 2 √(x)`
x+ 1 = 7 - 2√2
roots​

Answer 1

Answer: The equation has a solution .

Explanation:

Since we have given that

`√(x+1)=7-2√(x)`

Squaring on both the sides, we get that,

`x+1=(7-2√(x))^2\\\\x+1=49+4x-28√(x)\\\\3x+48-28√(x)=0`

Let
`√(x)=y\implies x=y^2`

So, our equation becomes,

`3y^2-28y+48=0\\\\y=(14)/(3)\pm (2√(13))/(3)\\\\√(x)=(14)/(3)\pm (2√(13))/(3)\\\\x=((14)/(3)\pm (2√(13))/(3))^2`

So,
`x=(248)/(9)\pm (56√(13))/(9)`

Hence, the equation has a solution .