Advanced MathVery hardDifference of two numbers from their sum and sum of squares
Advanced Math practice question
If x + y = 8, x² + y² = 34, and x > y, what is the value of x − y?
Answer: 2
(x − y)² = 2(x² + y²) − (x + y)² = 68 − 64 = 4, so x − y = 2 since x > y.
Common wrong answers
- If you answered 4
- 4 is (x − y)², not x − y.
- If you answered 15
- 15 is xy.
- If you answered -2
- −2 is ruled out because x > y.
More Advanced Math questions
- Very hard
The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b? - Very hard
What is the solution to the equation 6/(x − 2) = 3? - Very hard
The polynomial p(x) = x³ − 4x has how many distinct real zeros? - Very hard
The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of… - Very hard
The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a… - Very hard
In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…
Not affiliated with the College Board. SAT is a trademark of the College Board.