Question

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

Answer 1

let 1 no be x
another number be y
therefore sum of the squares of 2 nos(x&y) is given by. x2+y2=233. -1
one of the no(x) is 3 less than twice the other no(y)
x=2y-3. -2
substitute 2 in 1
we get,
(2y-3)2+y2=233
4y2+9-12y=233
4y2-12y=224
4y2-12y-224=0
take 4 common
the equation becomes
y2-3y-56=0
by the formula
see top
next x=2 ×3+root (233)/2-3
x=root (233) will be the answer
For y u see image