1. x = 4
2. x = 3
3. x = 2 and x = -3
Step-by-step explanation:
solution 1
[tex]\sqrt{3x+4}[/tex] = 4
or, 3x+4 = 16 ( by squaring both sides)
or, 3x = 16 - 4
or, 3x = 12
or, x = 12/3
=4
solution 2
(x+5)^(2/3) = 4
or, (x+5) = 4^(3/2) ( by the rule of index)
or, x+5 = 2^3
or, x + 5 = 8
or, x = 8 - 5 = 3
solution 3
[tex]\sqrt{x+7}[/tex] - x = 1
or, [tex]\sqrt{x+7}[/tex] = x+1
or, x + 7 = (x+1)^2 (squaring both sides)
or, x + 7 = [tex]x^{2}[/tex] + 2x +1
or, [tex]x^{2}[/tex] + x - 6 = 0
or, [tex]x^{2}[/tex] + 3x - 2x - 6 = 0 ( by middle term factor method)
or, (x+3) (x -2) = 0
or, x= -3 and x = 2
