Question

What is the sum of two consecutive even numbers, the difference of whose squares is 84?
s. One number is 7 more than another and its square is 77 more than the square of the smaller number.
What are the numbers?
The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the​

Answer 1

Answer:

Let the number be [math]x[/math] and [math]x + 2[/math]

A.T.Q,

[math] (x+2)^2 - x^2 = 84[/math]

Now use basic formula of [math]a^2 - b^2 = (a+b)(a-b)[/math]

[math]\implies (x+2+x)\cdot 2 = 84[/math]

[math]\implies (2\cdot x+ 2) = 42[/math]

[math]\implies 2\cdot x = 40[/math]

[math]\implies x = 20[/math]

Hence First number is [math]20[/math] and Second number is [math]22( x+2)[/math]

Your answer will be, [math]x + x + 2 = 20 + 22 = 42[/math]