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What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3x-1)?
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What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3...
Explanation of the problem
The problem states that we need to find the value of 5xy given that X^2 + 10y^2 + 1 is smaller than or equal to 2y(3x-1). We need to solve this inequality to determine the range of values that x and y can take and then use those values to find the value of 5xy.
Solving the inequality
To solve the inequality, we first simplify the expression on the right-hand side:
- 2y(3x-1) = 6xy - 2y
Now we can rewrite the inequality as:
- X^2 + 10y^2 + 1 <= 6xy="" -="">
Next, we move all the terms to one side:
- X^2 - 6xy + 10y^2 - 2y + 1 <=>
We can factor the quadratic expression to get:
- (x-2y+1)(x-5y+1) <=>
Now we need to determine the range of values for x and y that satisfy this inequality. We can do this by considering the signs of each factor:
- If both factors are positive or both are negative, the inequality is not satisfied.
- If one factor is zero, the inequality is satisfied. This occurs when x = 2y-1 or x = 5y-1.
- If x-2y+1 is negative and x-5y+1 is positive, the inequality is satisfied. This occurs when x < 2y-1="" and="" x="" /> 5y-1.
- If x-2y+1 is positive and x-5y+1 is negative, the inequality is satisfied. This occurs when 2y-1 < x="" />< />
Finding the value of 5xy
Now that we have determined the range of values for x and y that satisfy the inequality, we can find the value of 5xy by substituting the values of x and y into the expression:
- When x = 2y-1, 5xy = 5(2y-1)y = 10y^2 - 5y
- When x = 5y-1, 5xy = 5(5y-1)y = 25y^2 - 5y
We can see that as y increases, the value of 5xy increases as well. Therefore, the maximum value of 5xy occurs when y is at its maximum value, which is when y = 1/10. Substituting this value into the expression for x, we get:
- When x = 2(1/10)-1 = -8/10, 5xy = 10(1/10)^2 - 5(1/10) = 1/2 - 1/
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What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3...
Questions is wrong plz maintain appropriate symbols then upload
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What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3x-1)? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3x-1)? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3x-1)?.
What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3x-1)? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3x-1)? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of 5xy if X^2 10y^2 1 is smaller than equal to 2y (3x-1)?.
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