Question

5. One number is 7 more than another and its square is 77 more than the square of the smaller number. What are the numbers?
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Answer 1

Step-by-step explanation:

let one number be x

other no =x+7

(x+7)² -77 =x²

x²+49+14x-77=x²

x²-28+14x=x²

x²-x²+14x = 28

14x= 28

x= 2

other no = x+7 =2+7 =9

the numbers are 2 and 9

Answer 2

Given :-

• One number is 7 more than another and its square is 77 more than the square of the smaller number.

To Find :-

• The numbers = ?

Answer :-

• The required numbers are 2 and 9

Explaination :-

• Let one number be x and

• other number :- x + 7

★ According to Question :-

→ (x + 7)² - 77 = x²

→ x² + 49 + 2(x)(7) - 77 = x²

→ x² + 49 + 14x - 77 = x²

→ 49 + 14x - 77 = x² - x²

→ 14x - 28 = 0

→ 14x = 28

→ x = 28 ÷ 14

→ x = 2

Hence,

• One number = x = 2
• Other number = x + 7 = 2 + 7 = 9