Question

Difference of two numbers is 16. difference of their squares is 4000. find the two numbers.

Answer 1

let the numbers be a and b
$a - b = 16 ...(1)\\ {a}^{2} - {b}^{2} = 4000 \\ (a + b)(a - b) = 4000 \\ (a + b)(16) = 4000 \\ (a + b) = 250...(2) \\ add \: (1)and(2) \\ 2a = 266 \\ a = 133 \\ from(1) \\ b = a - 16 \\ b = 133 - 16 = 117$
therefore nos. are 133 and 117
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Answer 2

Answer:

The required numbers are 133 and 117.

Step-by-step-explanation:

Let the greater number be x.

And the smaller number be y.

From the first condition,

x - y = 16 - - - ( 1 )

From the second condition,

x² - y² = 4000

➞ ( x + y ) ( x - y ) = 4000 - - -

[ a² - b² = ( a + b ) ( a - b ) ]

➞ ( x + y ) × 16 = 4000 - - - [ From ( 1 ) ]

➞ x + y = 4000 / 16

➞ x + y = 250 - - - ( 2 )

Adding both equations, we get,

x - y = 16 - - - ( 1 )

x + y = 250 - - - ( 2 )

____________

➞ 2x = 266

➞ x = 266 / 2

➞ $\boxed{\red{\sf\:x\:=\:133}}$

By substituting x = 133 in equation ( 1 ), we get,

x - y = 16 - - - ( 1 )

➞ 133 - y = 16

➞ - y = 16 - 133

➞ - y = - 117

➞ $\boxed{\red{\sf\:y\:=\:117}}$

The required numbers are 133 and 117.