Question

sum of 3 terms of an ap is 21and product of 1st and 3rd terms is exceeds 2nd term by 3 write ap


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Answer 1

Answer:

$ap \: \: \: \: \: is \: \: \: \: 7 - \sqrt{39} \: \: \: \: \: \: \: \: \: \: 7 \: \: \: \: \: \: \: \: \: \: \: \: 7 + \sqrt{39}$

Step-by-step explanation:

$let \: the \: 3 \: terms = x - y \: \: \: \: \: \: \: x \: \: \: \: \: \: \: x + y \\ \\ x - y + x + x + y = 21 \\ 3x = 21 \\ x = 7 \\ \\ (x - y)(x + y) = x + 3 \\ ( {7}^{2} - {y}^{2} ) = 7 + 3 \\ \\ 49 - {y}^{2} = 10 \\ {y}^{2} = 39 \\ \\ y = \sqrt{39} \\ \\ ap \: \: \: \: \: is \: \: \: \: 7 - \sqrt{39} \: \: \: \: \: \: \: \: \: \: 7 \: \: \: \: \: \: \: \: \: \: \: \: 7 + \sqrt{39}$