Question

sum of squares of two consecutive positive odd nos. is 650. find the numbers

Answer 1

Let two numbers are x and x+2, According to Q's: X^2+(x+2)^2= 650 => x^2+x^2+4x+4=650 => 2x^2+4x-646=0 => x^2+2x-323=0 => x^2+19x-17x-323=0 = > x(x+19)-17(x+19)=0 =>(x+19)(x-17)=0 => x=17 So numbers will be 17 and 19

Answer 2

Let:-

The first number be x

Then:-

Second number will be x + 2

According to Question:-

==> x² + (x +2)² = 650

==> x² + x² + 2² + 2*2*x = 650

==> 2x² + 4 + 4x = 650

==> 2x² + 4x = 650 - 4

==> 2x² + 4x = 646

==> 2x² + 4x - 646 = 0_______(i)

Now divide EQ. (i) by 2,

==> x² + 2x - 323 = 0

==> x² + 19x - 17x - 323 = 0

==> x (x + 19) - 17( x + 19) = 0

==> (x + 19) (x - 17) = 0

Here Case I,

==> x + 19 = 0

==> x = -19 ( we will not consider this)

Case II,

==> x - 17 = 0

==> x = 17

Hence:-

• The numbers are 17 and 19.