Question

manisha secored x marks in maths and y in physics . The value of x and y if x-y=2 and xy = 2600 is: A)50 and 52 B)68 and 26 C)51 and 54 D)36 and 52​

Answer 1

(x+y)² - (x-y)² = 4xy

Substitute known values

(x+y)² - 2² = 4×2600

(x+y)²   = 10404

(x+y) =  102...(1)

We already have

x-y = 2...(2)

Solve equations (1) and (2)

We get the answer as (A) 50 and 52.

This is correct method to solve.

But seeing the options itself, we can arrive at an answer easily. Because only in (A), the condition that x-y=2 is satisfied. In the remaining three options, x-y value is not equal to 2

Answer 2

Answer:

A) 50 and 52.

Step-by-step explanation:

Given:- x - y = 2 & xy = 2600

To Find:- The value of x and y.

Solution:-

⇒ x - y = 2      -------- (1)

⇒ x = 2 + y      

xy = 2600 -------- (2)

Putting x = 2 + y in eq (2), we get

⇒ (2 + y)y = 2600

⇒ $2y + y^{2} = 2600$

⇒ $y^{2} +2y-2600=0$

⇒ $y^{2} + (52-50)y-2600=0$

⇒ $y^{2} +52y-50y-2600=0$

⇒ $y(y+52)-50(y+52)=0$

⇒ $(y+52)(y-50)=0$

⇒ $y=-52, 50$

Since, marks cannot be negative.

Therefore, y = 50.

Putting y = 50 in eq(1), we get

⇒ x = 2 + 50

⇒ x = 52.

Therefore, the value of x is 52 and y is 50.

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