Two numbers x and are in GP and their sum is 30. Also the sum of their square is 468. Find the numbers.

Two numbers x and are in GP and their sum is 30. Also the sum of their square is 468. Find the numbers.

Recent math Solution
Recent math Solution

 

Solution:

Let, X = a
Common ratio = r
So, Y = ar
1st condition,  X+ Y= 30
Or, a + ar =30
Or, ar = 30 – a
From 2nd condition,
a2+(30-a)2= 468
Or, a2 + 900-60a+a2=468
Or, a2-12a- 18a+ 216 = 0
Or, a(a-12) -18(a-12) = 0
Or, (a-12)(a-18) = 0
Or, a= 12, 18
So, ar = 18, 12
Answer: (X,Y) =(12, 18),(18, 12)
Two numbers x and are in GP and their sum is 30. Also the sum of their square is 468. Find the numbers. Two numbers x and are in GP and their sum is 30. Also the sum of their square is 468. Find the numbers. Reviewed by Admin on 7:37 PM Rating: 5

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