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The sum of a number and its positive square root is 6/25. Find the number.
The sum of a number and its positive square root is 6/25. Find the number.
Given: The sum of a number and its positive square root is 6/25.
To find: the number.Solution:Let the number be ‘a’.
⇒ a + √a = 6/25
⇒ √a = (6/25) – a
Squaring both sides
⇒ a = 36/625 + a2 – 12a/25
⇒ a2 – 37a/25 + 36/625 = 0
factorise by splitting the middle term.
⇒ a2 – a/25 – 36a/25 + 36/625 = 0
⇒ a(a – 1/25) – (36/25) × (a – 1/25) = 0
⇒ (a – 36/25)(a – 1/25) = 0
⇒ a = 36/25 , 1/25
But only 1/25 is possible as its sum with its positive root is 6/25.
Hence the number is 1/25.
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let no = x2\xa0x +{tex}\\sqrt{x}{/tex}\xa0= 6/25×2 + x = 6/25\xa025x2 + 25x=625×2 + 25x – 6 =025×2 + 30x – 5x – 6-05x( 5x + 6) – (5x + 6) =05x + 6 =0\xa0x = -6/5 or x = 1/5thus no is (1/5)2 = 1/25\xa0
Are gitika kaha ho
Nahi gitika the write answer is 1/25
1/5