Class 10

Math

All topics

Quadratic Equations

The difference of square of two numbers is $45$ and square of the smaller is $4$ times the larger number. Find two numbers.

according to question $x_{2}−y_{2}=45$ and $y_{2}=4x$

from both equation $x_{2}−4x=45$

$⇒x_{2}−4x−45=0$

$⇒x_{2}−9x+5x−45=0$

$⇒x(x−9)+5(x−9)=0$

$⇒(x−9)+(x+5)=0$

$⇒x−9=0$

$⇒x=9$

Larger number $(x)=9$

square smaller number $=4×9=36$

Smaller no. $±36 ±6$

Hence, number are $9,6$ or $9,6$