Question

multiplication of two numbers is 162 and the division is 2. find the numbers. ​

Answer 1

Answer:

The sum of the squares of two numbers is 162. The product of the two numbers is 81. Find the numbers.

Let x = one of the numbers

Let y= the other number

We have 2 unknowns so we need two equations relating the unknowns:

The sum of the squares of two numbers is 162: x2 + y2 = 162

The product of the two numbers is 81: x*y = 81

From the second equation, y = 81/x

Let's substitute 81/x in place of y in the first equation.

x2 + y2 = 162

x2 + (81/x)2 = 162

x2 + 6561/x2 = 162

x4 - 162x2 + 6561 = 0 [Multiplied both sides by x2]

Let u = x2

u2 - 162u + 6561 = 0

(u-81)2 = 0

u = x2 = 81

x = ±9

(x,y) = (9,9) and (-9,-9)