The sum of three terms in an AP is 9root2 If the sum of their squares is 118, then the product of these
three terms is
Answers
Given : sum of three terms in an AP is 9√2
sum of their squares is 118,
To Find : product of these three terms
Solution:
Let say three terms are
a - d , a , a + d
sum of three terms in an AP is 9√2
a - d + a + a + d = 9√2
=> 3a = 9√2
=> a = 3√2
sum of their squares is 118,
=> (a - d)² + a² + (a + d)² = 118
=> a² + d² - 2ad + a² + a² + d² + 2ad = 118
=> 3a² + 2d² = 118
=> 3(3√2)² + 2d² = 118
=> 3(18) + 2d² = 118
=> 2d² = 64
=> d² = 32
Product of three terms
(a - d)a( a+ d)
= a(a² - d²)
= 3√2 ( 18 - 32)
= 3√2 (-14)
= -42√2
product of these three terms is -42√2
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