Class 10

Math

All topics

Quadratic Equations

Divided $16$ into two parts such that $2$ times the square of the larger part is $164$ more than the square of the smaller part.

$x+y=16$ ……..$(1)$

$2x_{2}=y_{2}+164$ ……..$(2)$

Put $y=16−x$

$2x_{2}=(16−x)_{2}+164$

$2x_{2}=x_{2}+256−32x+164$

$x_{2}=420−32x$

$x_{2}+32x−420=0$

$x_{2}+42x−10x−420=0$

$x(x+42)−10(x+42)=0$

$(x−10)(x+42)=0$

$x=10$ x can't be $−42$ since its largest

$y=16−10=6$.