Question

Solve the given equations:
√(x+5) +√(x+12) =√2x+41​

Answer 1

Step-by-step explanation:

x+5+x+12=2x+41

2x+17=2x+41

24 is the answer

Answer 2

Step-by-step explanation:

SOLUTION

Here given Equation is

\sqrt{(x + 5)} + \sqrt{(x + 12)} = \sqrt{2x + 41}

Squaring both the sides, we get

= > (x + 5) + (x + 12) + 2 \sqrt{(x + 5)(x + 12)} =2x + 41 \\ = > 2 \sqrt{(x + 5)(x + 12)} = 24 \\ = > \sqrt{(x + 5)(x + 12)} = 12

Again squaring both the sides, we get

= > (x + 5)(x + 12) = 144 \\ = > {x}^{2} + 17x + 60 = 144 \\ = > {x}^{2} + 17x - 84 = 0 \\ = > {x}^{2} + 21x - 4x - 84 = 0 \\ = > x(x + 21) - 4(x + 21) = 0 \\ = > (x + 21)(x - 4) = 0 \\ so \\ = >x = - 21 \: \: \: and \: \: \: x = 4

Solving for x = 4 is a root, because it satisfy the given Equation. Also x= -21 is an extraneous root because it does not satisfy the given Equation.

hope it helps ✔️