Review question

# Can we solve $\sqrt{4x+13}-\sqrt{x+1}=\sqrt{12-x}?$ Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6431

## Suggestion

1. Solve $\sqrt{4x+13}-\sqrt{x+1}=\sqrt{12-x}.$

How could we get rid of the square roots?

Squaring both sides of this will still leave a square root, but could we rearrange and square again?

If we do this, will our solutions all be valid?

1. One root of the equation $3x^3+14x^2+2x-4=0$ is rational. Obtain this root and complete the solution of the equation.

What does the question mean by ‘rational’?

We could write this root as $\dfrac{a}{b}$, where the fraction is in lowest terms. What happens if we substitute this into the cubic and simplify?

Since $a$ and $b$ have no common factors, what does this tell us?

Can you find any ways to minimise the number of possibilities for $a$ and $b$ that need checking? Can we then check all the possibilities?