math please!! 12

Question

solve a) √(7x)=5    b)√(4x-5)=6     c) √6x+7 = √ 7x+7+6

Answer 1

a) The radical equation √(7x) = 5

Squaring on each side.

[√(7x)]² = 5²

7x = 25

Divide each side by 7.

x = 25/7

Solution x = 25/7.

Answer 2

b) The radical equation √(4x - 5) = 6

Squaring on each side.

[√(4x - 5)]² = 6²

4x - 5 = 36

4x = 36 + 5

4x = 41

x = 41/4

Solution x = 41/4.

Answer 3

(c)

√(6x+7) = √ (7x+7) + 6

Square on both sides.

(√(6x+7))² = (√(7x+7) + 6)²

6x + 7 = 7x + 7 + 36 +12√(7x+7)

7x - 6x + 36 =  - 12√(7x+7)

x + 36 = -12√(7x+7)

Square on both sides.

(x + 36)² = 144(7x + 7)

x² + 1296 + 72x = 1008x + 1008

x² - 936x + 288 = 0

Roots of the Equation

Therefore the values of x are 468 ± 84√31.