Question Details

If t=6+3, find t266.

Options

A

3

B

5

C

9

D

15

Show Answer

Correct Answer :

Option D

15

Solution :

The correct option is 15.

We are given the value of t as:

t=6+3


We need to evaluate the expression t266.


Step 1: Calculate t2

Substitute t=6+3 into t2:

t2=6+32


Using the algebraic identity a+b2=a2+2ab+b2, where a=6 and b=3:

t2=62+2·6·3+32

t2=6+66+9

t2=15+66


Step 2: Substitute t2 into the given expression

Now, substitute the value of t2 into t266:

t266=15+6666


The term 66 cancels out:

t266=15


Thus, the final answer is 15.

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