PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
10th Edition
ISBN: 9780136174318
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter P, Problem 66RE
Solution
The solution of the given inequality.
(−∞,2−√53)∪(2+√53,∞)
Given information:
The inequality given is:
9x2−12x−1>0 .
Formula used:
- To solve an quadratic inequality follow the steps:
- Find roots of quadratic corresponding equation.
- Divide the interval using the roots.
- Check in for which interval the inequality satisfy.
- Quadratic formula to solve an equation ax2+bx+c=0, is x=−b±√b2−4ac2a
Calculation:
In order to solve the given inequality:
9x2−12x−1>0
Take the corresponding
f(x)=9x2−12x−1
Now find it’s roots using the quadratic formula:
x=−b±√b2−4ac2a
Here,
a=9,b=−12, c=−1
Thus, the solution of the equation can be find as:
x=−b±√b2−4ac2ax=−(−12)±√(−12)2−4(9)(−1)2(9)x=12±√144+3618x=12±√18018x=12±6√518x=2±√53x=2−√53, and x=2+√53
Now use the roots above to divide the interval (−∞,∞) , as
(−∞,2−√53),(2−√53,2+√53), and (2+√53,∞)
Now check which interval satisfy the inequality by taking any value from these intervals and checking if
9x2−12x−1>0
for (−∞,2−√53)take x=−19x2−12x−1=9(−1)2−12(−1)−1=9+12−1=20>0
Thus, this is in solution, second check for
(2−√53,2+√53)take x=09x2−12x−1=9(0)2−12(0)−1=0−0−1=−1>0
Thus, this isn’t in the solution, now check for
(2+√53,∞)take x=29x2−12x−1=9(2)2−12(2)−1=36−24−1=11>0
Thus, this is in solution.
Thus, solution of given inequality is:
(−∞,2−√53)∪(2+√53,∞)
Chapter P Solutions
PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
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Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning