Question

Solve: Vx+1= Vx+6 -1
Squaring both sides of the equation results in
which of the following?
x+1= x + 6-1
x+1= x + 6 +1
x+1= x+7+2VX-6
x+1= x+7-2Vx+6

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

Answer 2

An equation is formed of two equal expressions. The correct option is D.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

For the given equation, squaring both sides of the equation will result in,

√(x+1)= √(x+6) -1

Squaring both sides,

[√(x+1)]²= [√(x+6) -1]²

x + 1 = [√(x+6)]² + 1² - [2×1×√(x+6)]

x + 1 = (x+6) + 1 - 2√(x+6)

x + 1 = x + 7 - 2√(x+6)

Hence, squaring both the sides of the equation √(x+1)= √(x+6) -1 will result in (x+1) = x+7-2√(x+6).

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