KnowledgeBoat Logo
|

Mathematics

Assertion (A) : If the volume of a cube is a3 + b3 + 3ab(a + b), then the edge of the cube is (a + b)

Reason (R) : (1st term + 2nd term)3 = (1st term)3 + 3(1st term)2 .(2nd term) + 3(2nd term)2 .(1st term) + (2nd term)3.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Identities

1 Like

Answer

Volume of a cube = (edge)3

⇒ (edge)3 = a3 + b3 + 3ab(a + b)

⇒ (edge)3 = (a + b)3

⇒ edge = (a+b)33\sqrt[3]{(a + b)^3}

⇒ edge = (a + b)

So, assertion (A) is true.

Using identity,

⇒ (a + b)3 = a3 + b3 + 3ab(a + b)

⇒ (a + b)3 = a3 + 3a2b + 3ab2 + b3

Substitute a = 1st term and b = 2nd term

(1st term + 2nd term)3 = (1st term)3 + 3(1st term)2 .(2nd term) + 3(2nd term)2 .(1st term) + (2nd term)3

So, reason (R) is true and, reason (R) is the correct explanation of assertion (A).

Hence, option 1 is the correct option.

Answered By

2 Likes

Related Questions