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Grade: 9
        
Please give answer
Find the ap or gp o. 
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2 months ago

Answers : (1)

Arun
22809 Points
							
a(1/b+1/c) + c(1/a+1/b) 
=a(c +b)/bc + c(a+b)/ab 
={a²(c +b) + c²(a+b)}/abc 
={a²c +a²b + c²a+c²b)}/abc 
={a²c+ c²a +a²b +c²b)}/abc 
={ac(a+c) +a²b +c²b)}/abc  
={ac(2b) +a²b +c²b)}/abc Since a,b,c are in AP hence a+c=2b 
={2abc +a²b +c²b)}/abc 
=b{2ac +a² +c²)}/abc 
=b{(a+c)²)}/abc 
={(a+c)²)}/ac 
={(a+c)(a+c))}/ac 
=(2b)(a+c))}/ac Since a,b,c are in AP hence a+c=2b 
=(2b)(1/c+1/a) 
hence a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P if a,b,c are in AP
2 months ago
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