Question

Which equation results from isolating a radical term and squaring both sides of the equation for the equation ?

Answer 1

We can solve for the equivalent expression of the given expression:
√(x+6) + √x = 8
First, we need to square both sides such as shown below:
((√x+6) + (√x) =8)²
(x+6) + x = 64
Perform transposition and combine similar terms
x + 6 + x =64
2x = 64 -6
x = 29

Answer 2

Answer:

Hence, the desired equation is:

$x+6=64+x-16\sqrt{x}$

Step-by-step explanation:

We are given a equation as:

$\sqrt{x+6}+\sqrt{x}=8$

We can also write this equation as i.e. we can isolate our radical term as:

$\sqrt{x+6}=8-\sqrt{x}$

Now on squaring both side of the equation we get:

$(\sqrt{x+2})^{2}=(8-\sqrt{x})^2$

We know that:

$(a-b)^2=a^2+b^2-2ab$

so, we get from the equation:

$x+6=8^2+(\sqrt{x})^2-2\times 8\times \sqrt{x}\\\\x+6=64+x-16\sqrt{x}$

Hence, the desired equation which is obtained as a result from isolating a radical term and squaring both sides of the equation for the equation is:

$x+6=64+x-16\sqrt{x}$