Answer:
x = 0 .
-20/19 (see below).
Explanation:
√(x + 1) + √5x = √(7x + 1)
Squaring both sides:
x + 1 + 5x + 2√(x + 1)√5x = 7x + 1
2√(x + 1)√5x = 7x +1 - 1 - x - 5x = x
Squaring both sides:
4(x + 1)(5x) = x^2
20x^2 + 20x - x^2 = 0
19x^2 + 20x) = 0
x(19x + 20) = 0
x = 0, -20/19.
If we substitute x = 0 into the original equation we get
√(0 + 1) + √5*0 = √(7*0 + 1)
1 = 1 so this is a true solution.
-20/19 :- √(-20/19 + 1) is not real so unless we allow complex square root this is extraneous.