Question

the difference of 2 number is 3 and the sum of their square is 89. Taking the smaller integer and x form a quadratic equation and solve it to find the integers. The integers are
please step by step explanation gived​

Answer 1

Step-by-step explanation:

x-y=3....a

x^2+y^2=89....b

find x and y

squaring both sides of eq. a

(x-y)^2=3^2

x^2+y^2-2xy=9

putting the value of x^2+y^2 from eq. b we get

89-2xy=9

89-9=2xy

2xy=80; xy=40...c

xy=40 and

x-y=3 from eq. a

x=3+y

putting the value of x in eq. c we get

(3+y)(y)=40

3y+y^2=40

y^2+3y-40=0

solving the quadratic equation..

y^2+8y-5y-40=0

y(y+8)-5(y+8)=0

(y-5)(y+8)=0

y=5; y= - 8

if y=5

x-y=3; x-5=3; x=3+5; x=8

if y= - 8

x-y=3; x-(-8)=3; x+8=3; x=3-8; x=-5