Question

one number is 7 more than another and its square is 77 more than the square of the of the smaller number. What are the numbers ?

Answer 1

hello users ......

solution:-
let,
first number be = x
and
second (smaller) number = y

According to given;
difference between numbers
=> x - y = 7 ....(1.)
=> x = y+7
and
difference between squares .....
=> x² - y² = 77

we know that:
a² - b² = (a+b)(a-b)

=>x² - y² = (x-y)(x+y)
=> 77 = 7×(x+y)
=> x+y = 11 .....(2.)
putting the value of x in (2.)

=> (y+7) + y = 11
=> 2y = 11 - 7 = 4
=> y = 2

putting value of y in (1.)
we get ,
x - 2 = 7
=> x = 9

hence;
first number (greater) = 9
and
second (smaller) number = 2 Answer

⭐✡ hope it helps ✡⭐