<span>difference between the numbers x-y=3 x-y=3 add y on both sides x-y+y=3+y x=3+y square of the smaller number=4 times the larger number y^2=4*x y^2=4(3+y) y^2=12+4y subtract 12 and 4y on both sides y^2-4y-12=12+4y-12-4y y^2-4y-12=0 on adding -6 and +2 we get -4 and multiplying -6and 2 we get -12 y^2 -4y-12=0 can be written as y^2-6y+2y-12=0 y(y-6)+2(y-6)=0 here 1st two terms y is common term and last two terms 2 is common term now y0--6 is common term (y-6)(y+2)=0 here equating these two terms with zero we get y value y-6=0 adding 6 on both sides y-6+6=0+6 y=6 y+2=0 subtract 2 on both sides y+2-2=0-2 y=-2 here we take only positive values y=6 only now x=3+y=3+6=9 x=9 and y=6 check this problem difference of these two numbers=9-6=3
two positive numbers differ by 5 means here positive numbers are x and y x-y=5 their sum is x+y square of their sum=(x+y)^2 (x+y)^2=169 here 169 can be written as 13^2 (x+y)^2=(13)^2 here powers equal then bases equal x+y=13 and x-y=5 solving these two equations we get x and y values x+y=13 x-y=5
