Question

quadratic equations a square minus a b into x square - 2 into a square minus b sin 2x + b square minus is equal to zero has equal roots then show that it is equal to zero a cube plus b cube plus c cube equals to 3 ABC​

Answer 1

Hence Proved............

Answer 2

Hence showed $a^3+c^3+b^3=3abc$

Step-by-step explanation:

Given : Quadratic equation $(c^2-ab)x^2-2(a^2-bc)x+b^2-ac=0$ has equal roots.

To find : Show that $a^3+b^3+c^3=3abc$ ?

Solution :

General form of quadratic equation is $Ax^2+Bx+C=0$

The roots are equal then $B^2-4AC=0$

On comparing with general form,

$A=c^2-ab$, $B=-2(a^2-bc)$ and $C=b^2-ac$

Substitute the value in the condition,

$(-2(a^2-bc))^2-4(c^2-ab)(b^2-ac)=0$

$4(a^4+b^2c^2-2a^2bc)-4(c^2b^2-ac^3-ab^3+a^2bc)=0$

$4a^4+4b^2c^2-8a^2bc-4c^2b^2+4ac^3+4ab^3-4a^2bc=0$

$4a^4-12a^2bc+4ac^3+4ab^3=0$

$4a(a^3-3abc+c^3+b^3)=0$

$a^3-3abc+c^3+b^3=0$

$a^3+c^3+b^3=3abc$

Hence proved.

#Learn more

If a + b + c is equals to zero then show that a cube plus b cube plus c cube is equals 3 ABC

https://brainly.in/question/6340964