Question

Check whether the following are quadratic equations :
(i)(x-2)² + 1 = 2x - 3
(ii) x(x + 1) + 8 = (x + 2) (x - 2)
(iv) x(2x+3)=x²+1
(m) (x+2)³=x³-4​

Answer 1

Answer:

(i)(x-2)² + 1 = 2x - 3

=> x²-4x+4+1=2x-3

=> x²-4x-2x+5+3=0

=> x²-6x+8=0

This is a quadratic equation.

(ii)x(x + 1) + 8 = (x + 2) (x - 2)

=> x²+x+8=x²-2x+2x-4

=> x+8=-4

=> x=-4-8 = -12

This is not a quadratic equation.

(iv) x(2x+3)=x²+1

=> 2x²+3x = x²+1

=> 2x²-x²+3x-1 = 0

=> x²+3x-1=0

This is a quadratic equation.

(m) (x+2)³=x³-4

=> x²+4x+4=x³-4

=> x²+4x+4+4-x³=0

=> x²+4x+8-x³=0

=> x³-x²-4x-8=0

This is not a quadratic equation.