Solve the equation
√4x-3 - √2x-5 = 2

Answer

x= 3 and 7

Step-by-step explanation:

√4x-3 - √2x-5=2

√4x-3=2+√2x-5

squaring both sides

(√4x-3)²=(2+√2x-5)²

4x-3=2²+2*2*(√2x-5)+(√2x-5)²

4x-3=4+4(√2x-5)+2x-5

4x-2x-3+5-4=4(√2x-5)

2x-2=4(√2x-5)

again squaring both sides

(2x-2)²=(4(√2x-5))²

(2x)²-2*2x*2+2²=16(2x-5)

4x²-8x+4=32x-80

4x²-8x-32x+4+80=0

4x²-40x+84=0

4(x²-10x+21)=0

x²-10x+21=0

x²-(7+3)x+21=0

x²-7x-3x+21=0

x(x-7)-3(x-7)=0

(x-7)(x-3)=0

now

x-7=0

x=7

x-3=0

x=3

Step-by-step explanation: