please solve

Question

 

solve

a) √(4+x²) - 4 = x

b) √(b+6) - √ (b+1) =1

Answer 1

(a)

√(4 + x²) - 4 = x

Add 4 to each side.

√(4 + x²) = x + 4

Square on both sides.

4 + x² = (x + 4)²

4 + x² = x² + 8x + 16

Rewrite Expression such that alike terms are on one side

x² + 8x - x² = 4 - 16

8x = -12

x = -12/8

x = -3/2

Therefore the value of x is -3/2.

Answer 2

(b)

√(b+6) - √(b+1) = 1

Square on both sides.

(√(b+6) - √(b+1) )² = 1

(√(b+6))² + (√(b+1)) - 2√(b+6)√(b+1) = 1

b + 6 + b + 1 -2[√((b+6)(b+1))] = 1

2b + 7 - 2√(b² + 7b + 6) = 1

2b + 7 - 1 = 2√(b² + 7b + 6)

2b + 6 = 2√(b² + 7b + 6)

b + 3 = √(b² + 7b + 6)

Square on both sides.

(b+3)² = b² + 7b + 6

b² + 9 + 6b = b² + 7b + 6

Rewrite Expression such that alike terms are on one side

7b - 6b = 9 - 6

b = 3

Therefore the value of b is 3.