Question : If the highest common factor (HCF) of x and y is 15, then the HCF of 36x2 – 81y2 and 81x2 – 9y2 is divisible by ________.
Option 1: 135
Option 2: 120
Option 3: 180
Option 4: 90
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Correct Answer: 135
Solution :
The factor
of 36x
2
– 81y
2
= 9 × (4x
2
- 9y
2
)
The
factor
of 81x
2
– 9y
2
= 9 × (9x
2
- y
2
)
So, the HCF of (36x
2
– 81y
2
) and (81x
2
– 9y
2
) is 9 as 9 is the only highest and most common factor of the given equation.
But it is also given that the highest common factor (HCF) of x and y is 15 which means one more factor is 15.
On multiplying 15 with 9, the HCF of 36x
2
– 81y
2
and 81x
2
– 9y
2
is determined which is divisible by itself as well.
⇒ 15 × 9 = 135
Hence, the correct answer is 135.
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