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Find the value of the square root of 19^2 + 19 + 20
November 14, 2024
The square root of 19 squared plus 19 plus 20 is calculated to be 20.
Find the value of (a + b)² given a² + b² = 29 and ab = 10.
November 13, 2024
To find (a+b)^2, given a^2 + b^2 = 29 and ab = 10, substitute the given values into the equation (a+b)^2 = a^2 + 2ab + b^2, resulting in (a+b)^2 = 49.
Evaluate the expression 3^3 / 3 / 3 / 3
November 13, 2024
The expression 3³ ÷ 3 ÷ 3 simplifies to 1.
Solving a cubic equation
November 13, 2024
The only real solution to the cubic equation a^3 + a^2 - 36 = 0 is a = 3.
Solve for X in the equation X^3 - X^0 = 26
November 13, 2024
The solution to the equation X^3 - X^0 = 26 is X = 3.
Calculate the determinant of a 4x4 matrix.
November 12, 2024
The determinant of the given 4x4 matrix is calculated using cofactor expansion along the fourth row, resulting in a determinant of -21.
Calculate the determinant of a 2x2 matrix.
November 12, 2024
The determinant of the 2x2 matrix [[2, 2], [3, 5]] is calculated as (2 * 5) - (2 * 3) = 4.
Solving an equation with absolute value and exponent
November 12, 2024
The equation (x-1)^(|x|-4) = 1 has solutions x = -4, 0, 2, and 4.
Calculate the difference of 100 squared and 99 squared.
November 12, 2024
The difference of squares formula is used to evaluate the expression 100^2 - 99^2, resulting in 199.