Question

A number is 7 less than the other and its square is 77 less than the square of the greater number.The smaller number is:​

Answer 1

Answer:

Step-by-step explanation:

Given :-

A number is 7 less than the other number.

Its square is 77 less than the square of the greater number.

To Find :-

The Smaller Number

Solution :-

let the greater number be x

And the smaller number be x + 7

According to the Question,

⇒ (x + 7)²  - 77 = x²

⇒ x² + 49 + 14x - 77 = x²

⇒ x² - 28 + 14x = x²

⇒ x²- x² + 14x = 28

⇒ 14x = 28

⇒ x = 28/14

⇒ x = 2

greater number  = x = 2

smaller number = x + 7 = 2 + 7 = 9

Hence, the smaller number is 9.

Answer 2

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

Let the greater number be "a" .

&

Let the smaller number be "a + 7"

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A.T.Q,

$\large \implies {\sf{(a \: + \: 7)^2 \: - \: 77 \: = \: a^2 }}$

$\large \implies {\sf{a^2 \: + \: 49 \: + \: 14a \: - \: 77 \: = \: a^2}}$

[Using Identity (a + b)² = a² + b² + 2ab]

$\large \implies {\sf{\cancel{a^2} \: + \: 49\: + \: 14a \: - \: 77 \: = \: \cancel{a^2}}}$

$\large \implies {\sf{49 \: - \: 77 \: + 14a \: = \: 0}}$

$\large \implies {\sf{-28 \: + \: 14a \: = \: 0}}$

$\large \implies {\sf{14a \: = \: 28}}$

$\large \implies {\sf{a \: = \: \frac{ \cancel{28}}{ \cancel{14}}}}$

$\large \implies {\sf{a \: = \: 2}}$

$\Huge{\boxed{\boxed{\sf{a \: = \: 2}}}}$

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