If x + y = 10 and xy = 21, what is the value of x² + y²?
Practice Questions
Q1
If x + y = 10 and xy = 21, what is the value of x² + y²?
49
59
61
41
Questions & Step-by-Step Solutions
If x + y = 10 and xy = 21, what is the value of x² + y²?
Step 1: Start with the equations given: x + y = 10 and xy = 21.
Step 2: We need to find the value of x² + y².
Step 3: Use the formula x² + y² = (x + y)² - 2xy.
Step 4: Substitute the value of x + y into the formula: (10)².
Step 5: Calculate (10)², which is 100.
Step 6: Now substitute the value of xy into the formula: 2 * 21.
Step 7: Calculate 2 * 21, which is 42.
Step 8: Now, subtract 42 from 100: 100 - 42.
Step 9: Calculate 100 - 42, which gives you 58.
Step 10: Therefore, the value of x² + y² is 58.
Algebraic Identities – The question tests the understanding of the identity x² + y² = (x + y)² - 2xy, which relates the sum and product of two variables to their squares.
Simultaneous Equations – The problem involves solving for variables using given equations, which is a common algebraic skill.
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