Question

If Log (a+b)/3 = 1/2(log a + Log b), then show that
a² +b²=7 ab.​

Answer 1

Step-by-step explanation:

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a^2+b^2=7ab

add 2ab to both sides

a^2+b^2+2ab=9ab

(a+b)^2=9ab

prove log(a+b)/3=(1/2)(loga+logb)

log(a+b)/3=(1/2)(logab)

log(a+b)/3=log(ab)^(1/2)

(a+b)/3=(ab)^(1/2)

square both sides

(a+b)^2/9=ab

(a+b)^2=9ab

9ab=9ab