Explanation

The equation is x² - 4 = 0.

x² = 4

x = ±2

There are two solutions: x = 2 and x = -2.

Explanation

a³ + b³ = (a + b)(a² - ab + b²) = (a + b)³ - 3ab(a + b)

Explanation

Given -1 < X < Y < 0, both X and Y are negative.

Let's analyze the expressions:

xy²: Since y² is positive (because squaring a number makes it positive), and x is negative, xy² is negative.

x²y: Since x² is positive, and y is negative, x²y is negative.

xy: Since both x and y are negative, xy is positive.

Comparing the signs:

xy is positive.

Both xy² and x²y are negative.

Since xy is positive and the others are negative, xy must be the greatest.

Now, comparing xy² and x²y:

Let's consider the magnitude:

|x| > |y| (since X < Y < 0)

xy² = x * y² (x is more negative, y² is positive)

x²y = x² * y (x² is positive, y is negative)

Given |x| > |y|, x² > y² (since both are positive after squaring)

x²|y| > |x|y² (since |y| < |x| and both x² and y² are positive)

x²y < xy² (both are negative, but x²y is more negative)

So, the order from least to greatest is:

x²y, xy², xy

Explanation

Let's say the number is x. Its reciprocal is 1/x.

x ÷ 1/x = x * x = x²

The answer is square of a number.

Explanation

Given:

36xy = 18xyz

Divide both sides by 18xy:

2 = z

Explanation

Given:

x + y = 3 ... (1)

y + z = 6 ... (2)

Subtract (1) from (2):

(y + z) - (x + y) = 6 - 3

z - x = 3

x - z = -3

Explanation

Given:

xy = 35

x + y = 12

To find x² + y²:

(x + y)² = x² + 2xy + y²

144 = x² + 2(35) + y²

144 = x² + 70 + y²

x² + y² = 144 - 70

= 74

Explanation

Given:

3x : 2y = 6 : 5

Cross-multiply:

(3x) × 5 = (2y) × 6

15x = 12y

Divide both sides by 3y:

5x/y = 4

x/y = 4/5

So, x : y = 4 : 5

Explanation

Given x + 1/x = 3

To find x³ + 1/x³:

(x + 1/x)³ = x³ + 3(x²)(1/x) + 3(x)(1/x)² + 1/x³

= x³ + 3x + 3/x + 1/x³

= x³ + 1/x³ + 3(x + 1/x)

(x + 1/x)³ = x³ + 1/x³ + 3(3)

27 = x³ + 1/x³ + 9

x³ + 1/x³ = 27 - 9

= 18

Explanation

Given equation:

3/x + 2/(x+1) = 1

Multiply both sides by x(x+1):

3(x+1) + 2x = x(x+1)

Expanding both sides:

3x + 3 + 2x = x² + x

Combine like terms:

5x + 3 = x² + x

Rearrange the equation:

x² - 4x - 3 = 0

Solve the quadratic equation:

x = (4 ± √(16 + 12)) / 2

x = (4 ± √28) / 2

x = (4 ± 2√7) / 2

x = 2 ± √7

The answer is 2 + √7 or 2 - √7.