Question

Solve the following. 6.
1) The sum of 3rd and 7th term of an A.P. is 6 and their product is 6. Find the first term and the common difference.

perfect answer will be marked as brainly ​

Answer 1

Step-by-step explanation:

Given that,

$t3 + t7 = 6 = t3 \times t7$

there are 2 unknown values are a and d. fortunately, there is a two-equation to solve.

$a \: + 2 \times d \: + \: a + 6 \times d \: = 6 = (a + 2 \times d)(a + 6 \times d)$

$2 \times a + 8 \times d = 6 = {a}^{2} + 8 \times a \times d + 12 \times {d}^{2}$

by solving this equation by any known method like substitution we can get

$a \: = 3 - 2 \sqrt{3} \: \: \: and \: \: \: d \: = \sqrt{3} \div 2 \: \: \: \\ or \\ \\ a \: = 3 + 2 \sqrt{3} \: \: \: and \: \: d \: \\\: = - \sqrt{3} \div 2$

Note: I assuming that you are capable of solving a quadratic equation and linear equation.

Hope you find this useful. also, remember A.P first term and the common difference is an irrational number. If you try to verify your result for an exact match then you will get approximately answer. Please first read some fact about irrational numbers then you will understand what I am trying to say you.

Thanks for your attention.