Question

If y=x²−5 and y²−m=x2n for all values of x, where m and n are constants, what is the value of m?

a) 25
b) 5
c) 10
d) 1

Answer 1

To find the value of m in the equation y²−m=x2n, substitute the expression for y from the first equation and compare the coefficients of the terms on both sides. The coefficient of the constant term on the left side is 25-m, so m = 25.

Step-by-step explanation:

To solve for the value of m in the equation y²−m=x2n, we can substitute the expression for y from the first equation. So, we have (x²−5)²−m=x2n. Expanding the square and simplifying, we get x⁴-10x²+25-m=x2n. Since this equation is true for all values of x, we can compare the coefficients of the terms on both sides of the equation. The coefficient of the constant term on the left side is 25-m. Therefore, m must be equal to 25 (option a)).