Question

difference between two numbers is 6 and difference between squares is 180 find the sum of the numbers​

Answer 1

let a, b be the numbers

a-b=6 ...(eqn. 1)

a^2-b^2=180

but, a^2-b^2=(a+b)*(a-b)=(a+b)*6...[using eqn. (1)]

therefore, a+b= 180÷6=30 ...(eqn. 2)

using eqn. (1) and (2),

(a+b)+(a-b)=30+6

2a=36

a=36÷2=18

therefore, b=a-6 [from eqn. (1)]

b=18-6=12

Answer: a=18, b=12

Answer 2

Step-by-step explanation:

Let one no. =x

other no.=y

acc to ques

x-y=6----1.

x^2-y^2=180------2.

from 1.

x=6+y

put x=6+y in 2.

(6+y)^2-y^2=180

36+y^2+12y-y^2=180.

[using(a+b)^2= a^2+b^2=2ab]

36+12y =180

12y=180-36

12y=144

y=144/12

y=12

Put y=12 in 1.

x-12=6

x = 6+12

x= 18

therefore,x=18

y=12