Given that a(a+b)=36 and b(a+b)=64, where a and b are positive, (a−b) equals:
2.8
3.2
−2.8
−2.5
A
2.8
B
−2.5
C
3.2
D
−2.8
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Solution
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Given, a(a+b)=36 and b(a+b)=64 By adding both, a(a+b)+b(a+b)=36+64 ⇒a2+ab+ab+b2=100 ⇒a2+2ab+b2=100 ⇒(a+b)2=100 ⇒a+b=10(a+b≠−10) Now replacing a+b value in above equation: ⇒a(10)=36 and b(10)=64 ⇒10a=36 and 10b=64 ⇒10(a−b)=36−64 ⇒10(a−b)=−28 ∴a−b=−2.8
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