Question

Solve: Vx+1= Vx+6 -1

Answer 1

Answer:

$x + 1 = x +7-2\sqrt{x+6}$

Step-by-step explanation:

$\sqrt{x+1}= \sqrt{x+6}-1$

Squaring both sides of the equation would give $(\sqrt{x+1} )^{2} =(\sqrt{x+6}-1 )^{2}$ which then simplifies to $x + 1 = x -2\sqrt{x+6}+7$

We can then subtract 7 from both sides to get $x-6=x-2\sqrt{x+6}$

Then we can subtract x from both sides, which cancel out and we get $-6 =-2\sqrt{x+6}$

Then we need to divide both sides by -2 to get $3=\sqrt{x+6}$

Then we need to square both sides $(3)^{2} =(\sqrt{x+6} )^{2}$ to get rid of the square root to get 9 = x + 6

Then finally subtracting 6 from both sides we get 3 = x