Question

Solve : √x+5 + √x = 15÷√x+5

Ans : 4​

Answer 1

x = 4

Explanation:

The equation given is a radical equation, we will solve using the steps below:

√x+5 + √x = 15÷√x+5

√x+5 + √x =
`(15)/(√(x+5) )`

Multiply both-side of the equation by
`√(x+5)`

`√(x+5)`(√x+5 + √x) =
`(15)/(√(x+5) )` ×
`√(x+5)` ----------------------------------(2)

Note

`√(x+5)` ×
`√(x+5)` = x +5

Also at the right-hand side of the equation
`√(x+5)` cancel-out
`√(x+5)` leaving us with just 15

so equation(2) becomes

x+5 +√x
`√(x+5)` = 15

subtract 5 from both-side of the equation

x+5-5 +√x
`√(x+5)` = 15-5

x +√x
`√(x+5)` = 10

subtract x from both-side of the equation

x-x +√x
`√(x+5)` = 10-x

√x
`√(x+5)` = 10-x

square both-side of the equation

(√x
`√(x+5)`) ² = ( 10-x)²

x (x+ 5) = ( 10-x)(10-x)

open the bracket

x² + 5x = 100 - 20x + x²

subtract x² from both-side of the equation

x² - x² + 5x = 100 - 20x + x² - x²

5x = 100 - 20x

collect like term

5x + 20x = 100

25x = 100

divide both-side of the equation by 25

25x/25 = 100 /25

x = 4