Question

The roots of the equation $(3-x{)}^4+(2-x{)}^4=(5-2x{)}^4$ are

• A. All real
• B. All are non real complex
• C. 2 real and 2 non real complex
• D. 3 are real & one non real complex

Answer 1

The correct option is C

2 real and 2 non real complex

Put a = 3-x, b = 2 -x $a^4+b^4=(a+b{)}^4$

$\Rightarrow$ 2ab $(2a^2+3ab+2b^2)=0$

a = 0 (or) b = 0 (or) $2a^2+3ab+2b^2=0$

i.e., 3-x = 0 or 2-x = 0 or $7x^2-35x+44=0$

solving we get $x=3,x=2,x=\frac{(35\pm i\sqrt{7})}{14}$