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Anonymous . 5 years, 5 months ago
Yogita Ingle 5 years, 5 months ago
Let common multiple is x
Then three number are x, 2x and 3x
As per given condition
x + 2x + 3x = 1359
6x = 1359
x = 1359/6 = 226.5
So, numbers are 226.5, 453, 679.5
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Posted by Saurabh Tripathi 5 years, 5 months ago
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Yogita Ingle 5 years, 5 months ago
Let nth term of the given AP be the first negative term.
AP = 24 , 21 , 18
Here,
First term ( a ) = 24
Commmon difference ( d ) = 21-24 = -4.
Then , Tn <0=> { a + ( n - 1 ) × d } <0
=> { 24 + ( n - 1 ) × -3 } <0
=> 27 - 3n <0
=> 27 < 3n
=> 3n > 27
=> n = 9.
n = 10
Hence,
The 10th term is the first negative term of the given AP.
Posted by Aastik Singh 5 years, 5 months ago
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Yogita Ingle 5 years, 5 months ago
Let us assume √2 is rational number.
a rational number can be written into he form of p/q
√2=p/q
p=√2q
Squaring on both sides
p²=2q²__________(1)
.·.2 divides p² then 2 also divides p
.·.p is an even number
Let p=2a (definition of even number,'a' is positive integer)
Put p=2a in eq (1)
p²=2q²
(2a)²=2q²
4a²=2q²
q²=2a²
.·.2 divides q² then 2 also divides q
Both p and q have 2 as common factor.
But this contradicts the fact that p and q are co primes or integers.
Our supposition is false
.·.√2 is an irrational number.
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