Question

Solve: $\sqrt{8+2x-x^2}=6-3x.$

• A. $[1,9]$
• B. $[1,2]$
• C. $[1,\frac{26}{10}]$
• D. $[1,\frac{28}{10}]$

Answer 1

The correct option is D $[1,\frac{28}{10}]$

Given:

$\sqrt{8+2x-x^2}=6-3x.$

Squaring both sides:

$⟹8+2x-x^2=(6-3x{)}^2.$

$⟹8+2x-x^2=36+9x^2-36x$

$⟹10x^2-38x+28=0$

Solving we get:

$x=1,\frac{28}{10}$