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0 votes
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in Arithmetic Progression by (43.0k points)
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If the sum of three numbers which are in A.P is 15 and the sum of the squares of the extremes is 58, then those numbers are 

A) 3, 6, 9 

B) 3, 5, 7

C) 2, 5, 8 

D) 2, 6, 7

2 Answers

+1 vote
by (57.0k points)
selected by
 
Best answer

Correct option is (B) 3, 5, 7

Let a - d, a, a+d are required three numbers in A.P.

Given that their sum is 15.

\(\therefore\) (a - d) + a + (a+d) = 15

\(\Rightarrow3a=15\)

\(\Rightarrow a=\frac{15}3=5\)

Also given that the sum of the squares of the extremes is 58.

\(\therefore(a-d)^2+(a+d)^2=58\)

\(\Rightarrow(5-d)^2+(5+d)^2=58\)    \((\because a=5)\)

\(\Rightarrow 2(5^2+d^2)=58\)            \((\because(a-b)^2+(a+b)^2=2(a^2+b^2))\)

\(\Rightarrow5^2+d^2=\frac{58}2=29\)

\(\Rightarrow d^2=29-5^2=29-25\)

\(=4=2^2\)

\(\Rightarrow d=2\)

\(\therefore a-d=5-2=3\)

\(a+d=5+2=7\)

Hence, the required numbers are 3, 5 and 7.

+1 vote
by (43.3k points)

Correct option is B) 3, 5, 7

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