Question

The sum of squares of 2 numbers is 233 and the one number is 3 less than the other number find the numbers

Answer 1

let the first no.be xother no.is  2x-3so (2x-3)^2+x^2 =2334x^2-12x+9+x^2=233on simplifying and transposing we get 5x^2-12x-224=0
Trying to factor by splitting the middle term 1.1     Factoring  5x2-12x-224 
The first term is,  5x2  its coefficient is  5 .The middle term is,  -12x  its coefficient is  -12 .The last term, "the constant", is  -224 
Step-1 : Multiply the coefficient of the first term by the constant   5 • -224 = -1120 
Step-2 : Find two factors of  -1120  whose sum equals the coefficient of the middle term, which is   -12 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -40  and  28                      5x2 - 40x + 28x - 224
Step-4 : Add up the first 2 terms, pulling out like factors :                    5x • (x-8)              Add up the last 2 terms, pulling out common factors :                    28 • (x-8)Step-5 : Add up the four terms of step 4 :                    (5x+28)  •  (x-8)             Which is the desired factorization
Equation at the end of step  1  : (x - 8) • (5x + 28) = 0x=8/-28/52x-3=15(if x=8)or -71/5(if x=-28/5)