Question

Find three numbers in AP whose Sum is 15 and the no
whose product is 35 find the number​

Answer 1

Answer:

I just can't solve this question but I tried this as it in pic....

Answer 2

Step-by-step explanation:

Let us assume three numbers as :

$(a - d), \: \: (a), \: \: (a + d)$

The Sum of three numbers is 15

$(a - d) + (a) + (a + d) = 15$

Then the First number ‘a’ is :

$(a - d) + (a) + (a + d) = 15 \\ a - d + a + a + d = 15 \\ a \cancel{ - d} + a + a + \cancel d = 15 \\ 3a = 15 \\ a = \frac{15}{3} \\ \boxed{ a = \underline{ \underline{\bf 5}}}$

The Product of three numbers is 35

$(a - d) \times (a) \times (a +d) = 35$

Then the Common difference ‘d’ is :

$(a - d)(a)(a + d) = 35 \\ (5 - d)(5)(5 + d) = 35 \\ 5(5 - d)(5 + d) = 35 \\ 5( {5}^{2} - {d}^{2} ) = 35 \\ 5(25 - {d}^{2} ) = 35 \\ 25 - {d}^{2} = 35 \div 5 \\ 25 - {d}^{2} = 7 \\ 25 - 7 = {d}^{2} \\ 18 = {d}^{2} \\ \sqrt{18} = d \\ \sqrt{9 \times 2} = d \\ \sqrt{ {3}^{2} \times 2 } = d \\ \boxed{ \underline{ \underline{ \bf 3 \sqrt{2}}} = d}$