The sum of three numbers in AP is 15 and sum of their squares is 147 . Find the numbers
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plz solve the last eq. and find z value then put ineq. 3 and find x then both value put in eq. 1 and find y value . it is your answer type .thanks plz do me as breallist que.
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Let (a - d) , a and (a + d) are three terms in AP.
A/C to question,
sum of terms = 15
(a - d) + a + (a + d) = 15
3a = 15 => a = 5 -------(1)
again, (a - d)² + a² + (a + d)² = 147b
=> 2(a² + d²) + a² = 147
=> 3a² + 2d² = 147
=> 3(5)² + 2d² = 147 [ from equation (1),
=> 75 + 2d² = 147
=> 2d² = 147 - 75 = 72
=> d² = 36
taking square root both sides,
d = ± 6
hence numbers are : (a - d) = 5 + 6 = 11
a = 5
(a + d) = 5 - 6 = -1
therefore , 11 , 5 , -1 are terms in AP.
A/C to question,
sum of terms = 15
(a - d) + a + (a + d) = 15
3a = 15 => a = 5 -------(1)
again, (a - d)² + a² + (a + d)² = 147b
=> 2(a² + d²) + a² = 147
=> 3a² + 2d² = 147
=> 3(5)² + 2d² = 147 [ from equation (1),
=> 75 + 2d² = 147
=> 2d² = 147 - 75 = 72
=> d² = 36
taking square root both sides,
d = ± 6
hence numbers are : (a - d) = 5 + 6 = 11
a = 5
(a + d) = 5 - 6 = -1
therefore , 11 , 5 , -1 are terms in AP.
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