Advanced MathVery hardDifference of squared radicals
Advanced Math practice question
For x > 0, the expression (√x + 1)² − (√x − 1)² is equivalent to k√x, where k is a constant. What is the value of k?
Answer: 4
(√x + 1)² = x + 2√x + 1 and (√x − 1)² = x − 2√x + 1; their difference is 4√x.
Common wrong answers
- If you answered 0
- 0 assumes the squares are equal.
- If you answered 1
- 1 comes from the constant terms, which cancel.
- If you answered 2
- 2 counts only one of the two 2√x terms.
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.