(1 + 1/x)(1 + 1/(x+1))(1 + 1/(x+2))(1 + 1/(x+3))
= ((x+1)/x)((x+2)/(x+1))((x+3)/(x+2))((x+4)/(x+3))
Notice that the denominators and numerators cancel out:
= (x+4)/x
(x - 2)(x + 3) = 0
This implies:
x - 2 = 0 or x + 3 = 0
x = 2 or x = -3
Given the equation 6x + 5(3 - 1.4x) = 1.7:
Step 1: Distribute and simplify
6x + 15 - 7x = 1.7
-x + 15 = 1.7
Step 2: Solve for x
-x = 1.7 - 15
-x = -13.3
x = 13.3
Solve the equation: 2x + 3 = 9 → 2x = 6 → x = 3.
The value of x = 3 satisfies the equation.
Given:
a = 2
b = 3
c = 1
Let's calculate the expression:
a² + 3c + 4ab²
= (2)² + 3(1) + 4(2)(3)²
= 4 + 3 + 4(2)(9)
= 4 + 3 + 72
= 79
Given k = 15:
(k-2) = 15 - 2
= 13
Now, calculate 180/k:
180/k = 180/15
= 12
Multiply (k-2) by 12:
13 × 12 = 156
Let's calculate:
= 3⁰ = 1
= 3¹ × 3² = 3 × 9 = 27
= 1 + 27 - 1/3
= 9
Let's break it down step by step:
1. (√9²+12²) = √(81+144) = √225 = 15
2. (-3)² = 9
3. 15 + 9 = 24
4. (-1 + 2 + 3) = 4, and 4³ = 64
5. 24 - 64 = -40
6. ³√-125 = -5 (since (-5)³ = -125)
7. -40 - (-5) = -40 + 5 = -35
