If \(\sqrt{4x-9}+\sqrt{4x+9}=\sqrt{25}+\sqrt{7}\), then find the value of \(x^2+17\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 33
The numbers under the roots on the left differ by 18, and so do 25 and 7 on the right. Matching \(4x+9=25\) and \(4x-9=7\) gives one value of \(x\); and since the left side grows as \(x\) grows, no other value of \(x\) can give the same sum.
\(4x+9=25\) gives \(x=4\)
Then \(4x-9=16-9=7\), so the left side is \(\sqrt{7}+\sqrt{25}\), the right side
\(x^2+17=16+17=33\)