If x2 + 1/25x2 = 67/8 find X+1/5x
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Answer:
√351 / 2√10
Step-by-step explanation:
x² + 1/25x² = 67/8
It can be written as
x² + (1/5x)² = 67/8
Use algebraic identity a² + b² = (a + b)² - 2ab
(x + 1/5x)² - 2(x)(1/5x) = 67/8
(x + 1/5x)² - 2/5 = 67/8
(x + 1/5x)² = 67/8 + 2/5
(x + 1/5x)² = ( 336 + 16 )/40
(x + 1/5x)² = 351/40
Taking square root on both sides
x + 1/5x = √(351/40) = √351 / √40 = √351 / 2√10
Therefore the value of x + 1/5x is √351 / 2√10.
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