Paragraph: Let (8+3 7 )²⁰= U + V and (8-3 7 )²⁰= W , where U is an integer and 0 Question: What is the value of ( U + V ) W ?

Step-by-step solution

We have, (8+3 7 )²⁰= U + V ....(i) and (8-3 7 )²⁰= W ....(ii) Here, o < W < 1 Now, adding equation (i) & (ii), we have, aligned & U + V + W =(8+3 7 )²⁰+(8-3 7 )²⁰ & =2 [ ²⁰ C ₀ 8²⁰+ ²⁰ C ₂ 8¹⁸ (3 7 )^2+ .+(3 7 )²⁰ ] aligned R.H.S. is an even number. Also, o < V < 1, o < W < 1 and U is an integer V + W is an integer V + W =1 aligned & (U+V) W=(8+3 7 )²⁰(8-3 7 )²⁰ = & [(8+3 7 )(8-3 7 )]²⁰ = & (64-63)²⁰=1²⁰=1 aligned