Mathematics
Assertion (A): 1133 + 153 is divisible by 98.
Reason (R): Factors of a3 + b3 are (a + b) and (a2 - ab + b2).
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Factorisation
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Answer
A is false, R is true.
Explanation
a3 + b3 = (a+b)(a2 - ab + b2)
1133 + 153 = (113 + 15)(1132 - 113 x 15 + 152)
= 128(12,769 - 1,695 + 225)
= 128 x 11,299
This means 1133 + 153 is not divisible by 98.
∴ Assertion (A) is false.
a3 + b3 = (a + b)3 - 3ab(a + b)
= (a + b)((a + b)2 - 3ab)
= (a + b)(a2 + b2 + 2ab - 3ab)
= (a + b)(a2 + b2 - ab)
∴ Factors of a3 + b3 are (a + b) and (a2 - ab + b2).
∴ Reason (R) is true.
Hence, Assertion (A) is false, Reason (R) is true.
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