Question

the summation of two numbers is 10 and cube difference is 2. The big number is ___​

Answer 1

Step-by-step explanation:

Let the two numbers be x and y

Note the difference between x and y is 2

so x - y = 2

=> x = y + 2 ----------------------- (1)

The sum of the squares is 10

x^2 + y^2 = 10--------------------(2)

Substitute equ (1) in (2)

(y+2)^2 +y^2 = 10

y^2 + 4y + 4 + y^2 = 10

2y^2 + 4y + 4 = 10

2y^2 + 4y - 6 = 0

Divide both side by 2

y^2 + 2y - 3 = 0

Solving the equation, we have

(y+3)(y-1) = 0

y = -3 or 1

When y = 1

x = 1 + 2 = 3

=> the value of x and y respectively are x=3 and y =1

Note also: when y = -3 , x = -1