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Find the number of integral values of x satisfying √(−x ^2 10x − 16 ) < x-2?="" />
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Find the number of integral values of x satisfying √(−x ^2 10x − 16 ...
Problem: Find the number of integral values of x satisfying √(−x^2 10x − 16) < />
Solution:
Step 1: Simplifying the inequality
-√(−x^2 10x − 16) < />
Squaring both sides, we get:
x^2 - 4x + 4 > -x^2 + 10x + 16
Simplifying, we get:
2x^2 - 14x - 12 < />
Dividing by 2, we get:
x^2 - 7x - 6 < />
Step 2: Factoring
We can factor the quadratic as:
(x - 1)(x - 6) < />
Step 3: Plotting the inequality
We can plot the inequality on a number line as follows:
<---o---o---o---o---o---o---o--->
-1 0 1 2 3 4 5 6 7
We need to find the values of x that satisfy the inequality (x - 1)(x - 6) < 0.="" these="" are="" the="" values="" of="" x="" that="" lie="" between="" the="" roots="" of="" the="" />
Step 4: Solving the inequality
-1 < x="" />< />
The integral values of x that satisfy the inequality are:
x = 0, 1, 2, 3, 4, 5
Answer: There are 6 integral values of x that satisfy the inequality.
Solution:
Step 1: Simplifying the inequality
-√(−x^2 10x − 16) < />
Squaring both sides, we get:
x^2 - 4x + 4 > -x^2 + 10x + 16
Simplifying, we get:
2x^2 - 14x - 12 < />
Dividing by 2, we get:
x^2 - 7x - 6 < />
Step 2: Factoring
We can factor the quadratic as:
(x - 1)(x - 6) < />
Step 3: Plotting the inequality
We can plot the inequality on a number line as follows:
<---o---o---o---o---o---o---o--->
-1 0 1 2 3 4 5 6 7
We need to find the values of x that satisfy the inequality (x - 1)(x - 6) < 0.="" these="" are="" the="" values="" of="" x="" that="" lie="" between="" the="" roots="" of="" the="" />
Step 4: Solving the inequality
-1 < x="" />< />
The integral values of x that satisfy the inequality are:
x = 0, 1, 2, 3, 4, 5
Answer: There are 6 integral values of x that satisfy the inequality.
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Find the number of integral values of x satisfying √(−x ^2 10x − 16 )
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Find the number of integral values of x satisfying √(−x ^2 10x − 16 ) for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the number of integral values of x satisfying √(−x ^2 10x − 16 ) covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of integral values of x satisfying √(−x ^2 10x − 16 ) .
Find the number of integral values of x satisfying √(−x ^2 10x − 16 ) for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the number of integral values of x satisfying √(−x ^2 10x − 16 ) covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of integral values of x satisfying √(−x ^2 10x − 16 ) .
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