If x-1/x=4 then the value of x+1/x is
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Answered by
2
Answer:
x + 1 / x = 2√5
Step-by-step explanation:
Given---> x - 1 / x = 4
To find ---> Value of x + 1 /x
Solution---> ATQ,
x - 1 /x = 4
Squaring both sides we get,
=> ( x - 1 / x )² = ( 4 )²
We know that,
( a + b )² = a² + b² + 2ab , applying it here,
=> x² + ( 1 / x² ) - 2 x ( 1 / x ) = 16
=> x² + 1 / x² - 2 = 16
=> x² + 1 / x² = 16 + 2
=> x² + 1 / x² = 18
Now , we have an identity,
( a - b )² = a² + b² - 2ab , we get,
( x + 1 / x )² = x² + 1 / x² + 2 x ( 1 / x )
= x² + 1 / x² + 2
= ( x² + 1 / x² ) + 2
= ( 18 ) + 2
( x + 1 / x )² = 20
Taking square root of both sides
=> x + 1 / x = √20
=> x + 1 / x = √4 × 5
=> x + 1 / x = 2 √5
Answered by
19
x+1|x=√5
#answerwithquality #bal
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