Translate to an equation:x + x2 = 30Solve for x:x2 + x - 30 = 0(x + 6)(x - 5) = 0x = 5, -6
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.
-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.
√x^10 = √(x^5)^2 = x^5
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.
It is (x + y)^3 - sqrt(5x + 3y) and there is no sensible simplification of this expression.
x=5
Translate to an equation:x + x2 = 30Solve for x:x2 + x - 30 = 0(x + 6)(x - 5) = 0x = 5, -6
There are two solution: -3 and +2.
1.6
square of 5=5*5=25 Now sum of 23 and square of 5=23+25=48 Now one third of sum of 23 and square of 5=48/3 =16 Hence 16 is answer
0.8333
X+5
The formula to sum a series of numbers is: sum = 1/2 x number_of_numbers x (first_number + last_number) So to sum the integers 5 to 500: From 5 to 500 there are 500 - 5 + 1 = 496 integers, so sum = 1/2 x 496 x (5 + 500) = 125240
x+5=7 -5 -5 x=2
The square of 5 = 5 x 5 =25 Double the square of 5 = 2 x (5 x 5) = 2 x 25 = 50
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.