Question

Find three numbers in AP whose sum is 15 and product is 80. Pleae tell as fast as possible and step by step expaination.
Pleaseeee tell it fast .​

Answer 1

Given :-

• Three no.s are in AP
• sum of numbers is 15
• product of numbers is 80

To find :-

• Three no.s in the AP

Solution :-

Let, the three no.s be

a - d , a , a + d

then,

$:\implies\sf{sum\:of\:no.s=15}$

$:\implies\sf{a-d+a+a+d=15}$

$:\implies\sf{3a=15}$

$:\implies\boxed{\underline{\underline{\sf{\pink{a=5}}}}}$

and

$:\implies\sf{product\:of\:no.s=80}$

$:\implies\sf{(a-d)(a)(a+d)=80}$

$:\implies\sf{a(a^2-d^2)=80}$

putting value of a

$:\implies\sf{5((5)^2-d^2)=80}$

$:\implies\sf{25-d^2=\frac{80}{5}}$

$:\implies\sf{-d^2=16-25}$

$:\implies\sf{-d^2=-(3)^2}$

$:\implies\boxed{\underline{\underline{\sf{\pink{d=3}}}}}$

Hence, the three no.s will be

↣  a - d = 5 - 3 = 2

↣ a = 5

↣ a + d = 5 + 3 = 8

Hence, the AP will be

2 , 5 , 8 .  

Answer 2

Answer:-

Let the numbers be a - d , a , a + d where a is the first term and d is the common difference.

Given:

Sum of the numbers = 15

→ a - d + a + a + d = 15

→ 3a = 15

→ a = 15/3

→ a = 5

And,

Product of the numbers = 80

→ (a - d) * (a + d) * (a) = 80

→ (a² - d²) * (a) = 80

[Since, (a + b)(a - b) = a² - b²]

Putting the value of a we get,

→ 5² - d² = 80/5

→ 25 - d² = 16

→ - d² = 16 - 25

→ - d² = - 9

→ d = √9

→ d = ± 3

If d = + 3,

→ a - d = 5 - 3 = 2

→ a = 5

→ a + d = 5 + 3 = 8

If d = - 3,

→ a - d = 5 - ( - 3) = 5 + 3 = 8

→ a = 5

→ a + d = 5 + (- 3) = 5 - 3 = 2.

Hence, the numbers are 2 , 5 , 8.