Solve : √x+5 + √x = 15÷√x+5

Ans : 4

x = 4

Step-by-step explanation:

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

√x+5 + √x = 15÷√x+5

√x+5 + √x  =

Multiply both-side of the equation by

(√x+5 + √x)  =  ×    ----------------------------------(2)

Note

 ×    = x +5

Also at the right-hand side of the equation   cancel-out   leaving us with just 15

so equation(2) becomes

x+5 +√x   = 15

subtract 5 from both-side of the equation

x+5-5 +√x   = 15-5

x +√x   = 10

subtract x from both-side of the equation

x-x +√x   = 10-x

√x   = 10-x

square both-side of the equation

(√x  ) 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

step-by-step explanation:

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