Question

the sum of the squares of two consecutive even number is 6500.which is the smaller number?

a.56
b.54
c.48
d.52​

Answer 1

Step-by-step explanation:

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Let two consecutive even numbers be x and x+2

According to condition

x^2+(x+2)^2=6500

x^2+x^2+4x+4=6500

2x^2+4x+4-6500=0

2x^2+4x-6496=0

Dividing the equation by 2 throughout

we get,

x^2+2x-3248=0

(But,3248=4×4×7×29

=2×2×2×2×7×29

=(2×29)×(2×2×2×7)

=58×56

But 58>56

So, 58 is positive and 56 is negative)

x^2+58x-56x-3248=0

x(x+58)-56(x+58)=0

(x+58)(x-56)=0

x=-58 or 56

But x can't be negative.

Therefore smaller number is 56.

Hope it helps you:)