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Question

If the A.M. of two positive numbers a and b (a > b) is twice their geometric mean. Prove that: a : b = (2+3) : (2-3).


Solution

 AM=2GM a+b2=2aba+b=4abSquaring both the sides:a+b2=4ab2a2+2ab+b2=16aba2-14ab+b2=0Using the quadratic formula:a=--14b+-14b2-4×1×b22×1     a is positive numbera=14b+2b49-12a=b7+43ab=7+43ab=4+3+2×2×3ab=2+32ab=2+322-32-3ab=2+34-32-3 ab=2+32-3

Mathematics
RD Sharma XI (2015)
Standard XI

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