The expression 79 + 97 is divisible by 64. - Mathematics

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MCQ
True or False

The expression 79 + 97 is divisible by 64.

Options

  • True

  • False

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Solution

This statement is True.

Explanation:

79 + 97 = (1 + 8)7 – (1 – 8)9

= `[""^7C_0 + ""^7C_1 * 8 + ""^7C_2 (8)^2 + ""^7C_3(8)^3 + ... + ""^7C_7(8)^7] - [""^9C_0 - ""^9C_1 8 + ""^9C_2 (8)^2 - ""^9C_3(8)^3 + ... ""^9C_9(8)^9]`

= (7 × 8 + 9  × 8) + (21  × 82 – 36  × 82) + …

= (56 + 72) + (21 – 36)82 + …

= 128 + 64 (21 – 36) + …

= 64[2 + (21 – 36) + …]

Which is divisible by 64

Concept: Proof of Binomial Therom by Combination
  Is there an error in this question or solution?
Chapter 8: Binomial Theorem - Exercise [Page 146]

APPEARS IN

NCERT Exemplar Mathematics Class 11
Chapter 8 Binomial Theorem
Exercise | Q 35 | Page 146
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