x=1/3+root 5 find the value of 16x^2 -14
Answers
Answered by
9
AnSwEr
- value of 16x²-14
First Step
we have to rationalize the given y
¶utting the value
Then
16x²-14
Answered by
2
Answer:
16x² - 14 = - 6√5
Solution:
- Given : x = 1/(3 + √5)
- To find : 16x² - 14 = ?
We have ;
x = 1/(3 + √5)
Now,
Rationalising the denominator of the term in RHS , we have ;
=> x = (3 - √5) / (3 + √5)(3 - √5)
=> x = (3 - √5) / (3² - √5²)
=> x = (3 - √5) / (9 - 5)
=> x = (3 - √5) / 4
=> 4x = 3 - √5
Now,
Squaring both the sides , we get ;
=> (4x)² = (3 - √5)²
=> 4²x² = 3² - 2•3•√5 + √5²
=> 16x² = 9 - 6√5 + 5
=> 16x² = 14 - 6√5
=> 16x² - 14 = - 6√5
Hence,
16x² - 14 = - 6√5 .
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