Question

Please solve this
$\sqrt{x - 5} - \sqrt{x - 8} = \sqrt{2x - 17}$

Answer 1

√(x−5​)-√(x−8)=√( 2x−17 )

[(√x-5)-(√x-8)]²=2x-17

[(x-5)+(x-8)-{2(√x-5)(√x-8)}]=2x-17

2x-13-2√[(x-5)(x-8)]=2x-17

2√[(x-5)(x-8)]=2x-2x-13+17

2√[(x-5)(x-8)]=4

√[(x-5)(x-8)]=2

(x-5)(x-8)=4

x²-8x-5x+40=2

x²-8x-5x+38=0

x²-13x+38=0

a=1
b=-13
c=38

x=-b+√b²-4ac/2a

x=13+√169-152/2

x=(13+√17)/2 or x=(13-√17)/2