If the sum of three numbers which are in A.P is 27 and the product of first and last is 77, then the numbers are
If the sum of three numbers which are in A.P is 27 and the product of first and last is 77, then the numbers are
A) 7, 10,11
B) 7, 9, 11
C) 6, 9, 12
D) 8, 9, 10
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Correct option is (B) 7, 9, 11
Let a - d, a & a+d are required three numbers that are in A.P.
Given that their sum is 27.
\(\therefore\) (a - d) + a + (a+d) = 27
\(\Rightarrow3a=27\)
\(\Rightarrow a=\frac{27}3=9\)
Also given that the product of first & last number is 77.
\(\therefore(a-d)(a+d)=77\)
\(\Rightarrow a^2-d^2=77\)
\(\Rightarrow d^2=a^2-77\)
\(=9^2-77\)
\(=81-77\)
\(=4=2^2\)
\(\therefore d=2\)
\(\therefore a-d=9-2=7\)
\(a+d=9+2=11\)
\(\therefore\) Required numbers are 7, 9 & 11.
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