Question

the difference between two number is 14 and the difference between their square is 448 then find the number

Answer 1

NICE QUESTION


X-Y=14
THEREFORE X=14+Y
X^2-Y^2=448
(14+Y)^2-Y^2=448
196+Y^2+28Y-Y^2=448
196+28Y=448
28Y= 252
Y=9
PUT Y IN (1)
X-Y=14
X-9=14
X=23


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Answer 2

Answer:

Required number are 23 and 9.

Step-by-step explanation:

Let two numbers are X and Y.

According to question,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x - y = 14 - - - - (1)$

$and \: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} - {y}^{2} = 448 - - - (2)$

$from \: formul \: {x}^{2} - {y}^{2} = (x + y)(x - y)$

$\: \: \: \: \: \: 448 = (x + y)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( from \: eqns.(1) \: and \: (2)$

$⇒ \: \: \: x + y = \frac{448}{14} = 32$

Now, on adding eqns. (1) and (3),

X - Y = 14

X + Y = 32

____________

2X = 46

$∴ \: \: \: \: \: x = 23$

On substituting the value of x in eqn. (1),

$\: \: \: 23 - y = 14$

$⇒ \: \: \: \: \: \: \: \: \: y = 23 - 14 = 9$

∴ Required number are 23 and 9.