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?
Solve the answer in a piece of paper and send it to me ​

Answer 1

Given:

• One number is 7 more than another number
• Square of one number is 77 more than the square of smaller number.

To find:

• What are these Number?

Solution:

Let one number be x.

∴ Another number is (x + 7)

★ Now, According to the Question:

→ (x + 7)² - 77 = x²

→ x² + 49 + 14x - 77 = x²

→ x² + 14x - 28 = x²

→ 14x = 28

→ x = 28/14

→ x = 2

Therefore,

• One number is 2
• Other number = (2 + 7) = 9

∴ Hence, the number numbers are 2 and 9.

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Verification:

Here,

Given that,

★ Square of one number is 77 more than the square of smaller number.

• (2)² = 4
• (9)² = 81

→ 4 + 77 = 81

Hence, Proved!

Answer 2

Correct Question-:

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

AnswEr -:

$\boxed{\sf{\blue{The \:number\: is\:-: x \:= 2 }}}$

$\boxed{\sf{\blue{The \:another \:number\: is\:-: x +7 \:= 2+7 = 9 }}}$

$\boxed{\sf{\blue{The \:number\: are\:-: \: 2\:and\:9 }}}$

Given,

• One number is 7 more than the other number.
• Square of one number is 77 more than the square of the smaller number.

To Find ,

• The numbers .

Solution,

• Let the number be x .

Then,

• The another number is x + 7 .

According to the question,

$\sf{\Rightarrow{\pink{(x+7)²-77 =x² }}}$

$\sf{\Rightarrow{\pink{x²+49 +14x -77 =x² }}}$

$\sf{\Rightarrow{\pink{x²+14x -28 =x² }}}$

$\sf{\Rightarrow{\pink{14x-28 =x²-x²+28}}}$

$\sf{\Rightarrow{\pink{14x =28}}}$

$\sf{\Rightarrow{\pink{x =\frac{28}{14}}}}$

$\sf{\Rightarrow{\pink{x =2}}}$

Therefore,

$\boxed{\sf{\blue{x = 2 }}}$

Hence ,

• $\boxed{\sf{\blue{The \:number\: is\:-: x \:= 2 }}}$
• $\boxed{\sf{\blue{The \:another \:number\: is\:-: x +7 \:= 2+7 = 9 }}}$

$\boxed{\sf{\blue{Hence \:,The \:number\: are\:-: \: 2\:and\:9 }}}$

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☆ Verification ☆

Given that ,

♤ Square of one number is 77 more than the square of the smaller number.

♧ (2)² -: 2 × 2 = 4

♧ (9)² -: 9 × 9 = 81

$\sf{\Rightarrow{\pink{4+77= 81}}}$

$\sf{\Rightarrow{\pink{81 = 81 }}}$

Therefore,

$\boxed{\sf{\blue{LHS = RHS }}}$

Hence Verified

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