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The sum of a number and its square is 30 find the numbers?
Translate to an equation:x + x2 = 30Solve for x:x2 + x - 30 = 0(x + 6)(x - 5) = 0x = 5, -6
Which is bigger the sum of the squares of 3 and 5 or the square of the sum of 3 and 5?
sum of squares: 32 + 52 = 9 + 25 = 34 square of sum (3 + 5)2 = 82 = 64 This is a version of the Cauchy-Schwarz inequality.
Square root of x to the tenth power?
√x^10 = √(x^5)^2 = x^5
What are two numbers whose sum -6 and product is -5?
-2 and -3Check:(-2) + (-3) = -5(-2)(-3) = 6Thus -2 and -3 are not the required numbers. let's find them: x + y = -6xy = -5 y = -x -6x(-x - 6) = -5-x^2 - 6x = -5x^2 + 6x = 5x^2 + 6x + 9 = 5 + 9(x + 3)^2 = 14x + 3 = (+ & -)square root of 14x = -3 (+ & -)square root of 14x = -3 + square root of 14 or x = - 3 - square root of 14y = -x - 6y = 3 - square root of 14 - 6 or y = 3 + square root of 14 - 6y = -3 - square root of 14 or y = -3 + square root of 14Check:(-3 + square root of 14) + (-3 - square root of 14) = -6(-3 + square root of 14)(-3 - square root of 14) = -5 ?(-3)^2 - (square root of 14)^2 = -5 ?9 - 14 = -5Check also tow other numbers.
How can you tell by drawing a factor tree whether or not a number is a square number?
A factor tree tells you the prime factorization. The prime factorization can indicate a square number. Square numbers have even pairs of prime factors. 2 x 2 x 3 x 3 is a square number. 5 x 5 x 5 x 5 x 7 x 7 x 7 x 7 is a square number.
