Question

If the sum of the squares of two
consecutive odd numbers is 74,then the
smaller number is?
1)11
2)3
3)7
4)5​

Answer 1

3) 7

Step-by-step explanation:

Smaller Integer is 5 and the other integer is 7

Let the smaller integer be X and the other one is ( X + 2)

X^2 + (X+2)^2 = 74

X^2 + X^2 + 4 X + 4 = 74

2 X^2 + 4 X = 74 - 4 = 70 or

X^2 + 2 X - 70 = 0 by resolving this quadratic equation we will get

( X + 7 ) ( X - 5 ) = 0 or

X = - 7 or 5 by ignoring the - 7 we will get

smaller integer be X = 5 and the other integer is 7

Answer 2

Answer:

5

Step-by-step explanation:

Let the first square of consecutive odd no.=x²

So, the second square of consecutive odd no.=(x+2)²

Now coming to the question,

x²+(x+2)²=74

=x²+x²+2²=74

=2x²+4=74

=2x²=74-4=70

=x²=70/2=35

=x=√35

=x=5.9

In the options the answer given is 5, so, the answer is 5.