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Mathematics

Assertion (A): If x > y, x + y = 6 and x - y = 2 then x2 + y2 = 40

Reason (R): (x + y)2 + (x - y)2 = 2(x2 + y2)

  1. A is true, but R is false.

  2. A is false, but R is true.

  3. Both A and R are true, and R is the correct reason for A.

  4. Both A and R are true, and R is the incorrect reason for A.

Expansions

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Answer

By formula,

⇒ (x + y)2 = x2 + y2 + 2xy ….(1)

⇒ (x - y)2 = x2 + y2 - 2xy …..(2)

Adding equation (1) and (2), we get :

⇒ (x + y)2 + (x - y)2 = x2 + y2 + 2xy + x2 + y2 - 2xy

⇒ (x + y)2 + (x - y)2 = 2(x2 + y2)

So, reason (R) is true.

Given,

x + y = 6 and x - y = 2

By formula,

⇒ 2(x2 + y2) = (x + y)2 + (x - y)2

⇒ 2(x2 + y2) = 62 + 22

⇒ 2(x2 + y2) = 36 + 4

⇒ 2(x2 + y2) = 40

⇒ x2 + y2 = 402\dfrac{40}{2}

⇒ x2 + y2 = 20.

So, assertion (A) is false.

∴ A is false, but R is true.

Hence, option 2 is the correct option.

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