Explanation

Let's denote the man's present age as x.

(x + 5) * 3 = 84

x + 5 = 84 / 3

x + 5 = 28

x = 28 - 5

x = 23

Explanation

Multiply the constants: 3 × 4 = 12.

Add the exponents of x: x² × x³ = x⁵, so the product is 12x⁵.

Explanation

area of rectangle garden=1500m²

length of garden=500m

width=x

area of rectangle = length *breadth

=1500=500*x

x=1500/500

x=3m

SH5-9-2023

Explanation

To solve |3x| = 6:

3x = 6 or 3x = -6

x = 2 or x = -2

Explanation

Given the quadratic equation x² + 2x - 2 = 0:

Step 1: Apply the quadratic formula

x = (-b ± √(b² - 4ac)) / 2a

Here, a = 1, b = 2, and c = -2.

Step 2: Calculate the roots

x = (-(2) ± √((2)² - 4_1_(-2))) / 2*1

x = (-2 ± √(4 + 8)) / 2

x = (-2 ± √12) / 2

x = (-2 ± 2√3) / 2

x = -1 ± √3

Explanation

Given x = 3 - √8:

Step 1: Find 1/x

To rationalize the denominator, first simplify √8 to 2√2.

x = 3 - 2√2

1/x = 1 / (3 - 2√2)

Multiply numerator and denominator by the conjugate (3 + 2√2):

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

= (3 + 2√2) / (9 - 8)

= 3 + 2√2

Step 2: Calculate x + 1/x

x + 1/x = (3 - 2√2) + (3 + 2√2)

= 6

Explanation

x + y is an expression because it shows a combination of variables and operations without an equal sign.

An equation must include an equal sign (e.g., x + y = 5).

Explanation

Given the equation x² - 3x - 4 = 0:

Step 1: Factor the quadratic equation

x² - 3x - 4 = (x - 4)(x + 1) = 0

Step 2: Solve for x

x - 4 = 0 or x + 1 = 0

x = 4 or x = -1

Explanation

The degree of the polynomial x^2yz^2+xyz+2 is 3.

Explanation

a² - b² = (a - b)(a + b)

a⁴ - b⁴ = (a² - b²)(a² + b²)

= (a - b)(a + b)(a² + b²)

The LCM is (a - b)(a + b)(a² + b²) = (a² - b²)(a² + b²)

= a⁴ - b⁴