Find the root of the equation √21 + 4x = x. if the equation has more than one root, indicate the largest.

We have an irrational equation. To solve it, you must first get rid of the square root. To do this, you need to square both the left side of the equation and the right side. And then solve the resulting equation. Let’s see what happens:

√ (21 + 4x) = x;

(√ (21 + 4x)) ^ 2 = (x) ^ 2;

21 + 4x = x ^ 2;

x ^ 2 – 4x – 21 = 0.

We find the roots of the resulting quadratic equation by Vieta’s theorem:

x1 = 7 – the largest root;

x2 = -3.

Answer: 7.

Verification:

√ (21 + 4 * 7) = 7;

√ (21 + 28) = 7;

√49 = 7;

7 = 7.