By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2024 Maths, question 46

Topic: Algebra

Passage · Q45 to Q46

Let (8+37)20=U+V(8+3\sqrt{7})^{20}=U+V and (8−37)20=W(8-3\sqrt{7})^{20}=W, where UU is an integer and 0<V<10<V<1.

Q46

What is the value of (U+V)W(U+V)W?

  1. (a) 1/21/2
  2. (b) 11Correct answer
  3. (c) 3/23/2
  4. (d) 22

Solution.

Answer: (b) 11

  1. Multiply the two conjugate powers.
  2. (U+V)W=[(8+3√7)(8−3√7)]²⁰=(64−63)²⁰=1.