Question

the sum of squares of two numbers is 233 and one of the number is 3 less than twice the other number find the numbers

Answer 1

Let The Numbers Be x And 2x-3.

Squares

x = x2

(2x-3)2 = 4x2-12x+9

Sum = x2+4x2-12x+9

5x2-12x+9 = 233

5x2-12x-224 = 0

Use Quadratic Formula

-b+Square Root (b2-4ac)/2a And -b-Square Root (b2-4ac)/2a

12+Square Root (144+4480)/10 And 12-Square Root (144+4480)/2a

12+68/10 And 12-68/10

8 And -56/10 = -28/5

As They Have Given Numbers So We Should Reject Fractions

So x = 8 And 2x-3 = 13

So Numbers Are 8 And 13