Question

Verify that: \[\sqrt{4x-7}+\sqrt{4x}=7\] Verify that: \[\sqrt{4x-7}+\sqrt{4x}=7\] @Mathematics

Answer 1

Do you mean find a solution? "Verify" generally means you want to prove is some statement is true or not.

Answer 2

I know that the solution is 4, but I do not know how to get 4 as an answer, but if it is verified I can easily find out how to accomplish this.

Answer 3

To find a solution, you would probably have to square the equation twice. This would create extraneous solutions though (4 being one of them), and you would have to test out which are correct/incorrect.

Answer 4

4 Does work as an answer, but I don't know how it is possible to get 4.

Answer 5

\[\left(\sqrt{4x-7}+\sqrt{4x}\right)^2=7^2\]\[\Longrightarrow4x-7+2\sqrt{4x(4x-7)}+4x=49\]\[\Longrightarrow \sqrt{4x(4x-7)}=28-4x\]Square again:\[4x(4x-7)=16x^2-224x+784\]\[\Longrightarrow16x^2-28x=16x^2-224x+784\]Lucky us, ths squared term cancels:\[-28x=-224x+784\Longrightarrow 196x=784 \Longrightarrow x= 4\]So in this particular example, we didnt have to worry about extraneous solutions.

Answer 6

What did you use to get this answer?

Answer 7

I just squared both sides twice. The idea is to get rid of the square roots.

Answer 8

I was just wondering if you used any type of calculator.

Answer 9

nope, all of that is basic algebra. pencil and paper to calculate squares (like 28^2).