Question

four numbers are in gp, the product of first and last number is 32. sum of the second and the third number is 12. find the numbers

Answer 1

Step-by-step explanation:

Given four numbers are in gp, the product of first and last number is 32. sum of the second and the third number is 12. find the numbers  

• Let the four numbers in G.P be a/r^3, a/r, ar,ar^3
• Now product of first and last number is 32
• So a/r^3 x ar^3 = 32
• So a^2 = 32
• Or a = 4√2
• Also sum of second and third number is 12
• So a/r + ar = 12
• Or a(1/r + r) = 12
• Or 4√2 (1/r + r) = 12
• Or 1/r + r = 3/√2
• So √2 + √2r^2 = 3r
•  √2 r^2 – 3r + √2 = 0
• √2 r^2 – 2r – r + √2 = 0
• √2 r (r - √2) – 1(r - √2) = 0
•     r - √2 = 0 or √2 r – 1 = 0
• Now r = √2 or r = 1 / √2
• Therefore the numbers are taking r = √2 and a = 4√2
• a / r^3 = 4√2 / (√2)^3 = 2
• a / r = 4
• ar = 8
• ar^3 = 16
• so the numbers are 2,4,8 and 16

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https://brainly.in/question/4309012