Question

Solve for x : 12x2 – 6(a2 + b2)x + 3a2b2 = 0.

Answer 1

Hope this picture helps you...  

Answer 2

The solution is $x=-\dfrac{b^2}{2},-\dfrac{a^2}{2}$

Step-by-step explanation:

Given : Quadratic equation $12x^2-6(a^2+b^2)x+3a^2b^2=0$

To find : Solve for x ?

Solution :

Using quadratic formula of equation $ax^2+bx+c=0$ is

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Quadratic equation $12x^2-6(a^2+b^2)x+3a^2b^2=0$

Here, a=12, $b=-6(a^2+b^2)$ and $c=3a^2b^2$

Substitute in the formula,

$x=\dfrac{-(-6(a^2+b^2))\pm\sqrt{(-6(a^2+b^2))^2-4(12)(3a^2b^2)}}{2(12)}$

$x=\dfrac{-6(a^2+b^2)\pm\sqrt{36(a^4+b^4+2a^2b^2)-144a^2b^2}}{24}$

$x=\dfrac{-6(a^2+b^2)\pm\sqrt{36a^4+36b^4+72a^2b^2-144a^2b^2}}{24}$

$x=\dfrac{-6(a^2+b^2)\pm\sqrt{36a^4+36b^4-72a^2b^2}}{24}$

$x=\dfrac{-6(a^2+b^2)\pm\sqrt{(6a^2)^2+(6b^2)^2-2(6a^2)(6b^2)}}{24}$

$x=\dfrac{(-6a^2-6b^2)\pm\sqrt{(6a^2-6b^2)^2}}{24}$

$x=\dfrac{(-6a^2-6b^2)\pm(6a^2-6b^2)}{24}$

$x=\dfrac{-6a^2-6b^2+6a^2-6b^2}{24},\dfrac{-6a^2-6b^2-6a^2+6b^2}{24}$

$x=\dfrac{-12b^2}{24},\dfrac{-12a^2}{24}$

$x=\dfrac{-b^2}{2},\dfrac{-a^2}{2}$

Therefore, the solution is $x=-\dfrac{b^2}{2},-\dfrac{a^2}{2}$

#Learn more

Solve:-( x÷9-x) =2÷7 solve

https://brainly.in/question/846166