Answer:
a²+1/a² = 7
Step-by-step explanation:
Given, a = (3+√5)/2
We have to find the value of a² + 1/a².
1/a = 1/((3+√5)/2) = 2/(3+√5)
By taking conjugate,
2/(3+√5) = 2/(3+√5) × (3-√5)/(3-√5)
= 2(3-√5) / (3+√5)(3-√5)
By using algebraic identity,
(a - b)(a + b) = a² - b²
(3+√5)(3-√5) = (3)² - (√5)²
= 9 - 5
= 4
2(3-√5) / (3+√5)(3-√5) = 2(3-√5) / 4
So, 1/a = (3-√5)/2
Now, a² = [(3+√5)/2]²
= (3+√5)²/4
By using algebraic identity,
(a + b)² = a² + 2ab + b²
(3+√5)² = (3)² + 2(3)(√5) + (√5)²
= 9 + 6√5 + 5
= 14 + 6√5
a² = (14+6√5)/4
= 2(7+3√5)/4
a² = (7+3√5)/2
Now, 1/a² = [(3-√5)/2]²
= (3-√5)²/4
By using algebraic identity,
(a - b)² = a² - 2ab + b²
(3-√5)² = (3)² - 2(3)(√5) + (√5)²
= 9 - 6√5 + 5
= 14 - 6√5
1/a² = (14-6√5)/4
1/a² = (7-3√5)/2
a²+1/a² = (7+3√5)/2 + (7-3√5)/2
= 7/2 + 3√5/2 + 7/2 - 3√5/2
= 7/2 + 7/2
= 7
Therefore, a²+1/a² = 7
Answer:
0.08
Step-by-step explanation:
![{5}^{ - 2} \times \sqrt[3]{8} \\ \\ = {5}^{ - 2} \times \sqrt[3]{ {2}^{3} } \\ \\ = \frac{1}{ {5}^{2} } \times 2 \\ \\ = \frac{1}{25} \times 2 \\ \\ = \frac{2}{25} \\ \\ =0.08](https://tex.z-dn.net/?f=%20%7B5%7D%5E%7B%20-%202%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B8%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%7B5%7D%5E%7B%20-%202%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B%20%7B2%7D%5E%7B3%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%7B5%7D%5E%7B2%7D%20%7D%20%20%5Ctimes%202%20%5C%5C%20%20%5C%5C%20%20%20%3D%20%5Cfrac%7B1%7D%7B25%7D%20%20%5Ctimes%202%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B2%7D%7B25%7D%20%5C%5C%20%5C%5C%20%3D0.08)
Answer:
x>-4
Step-by-step explanation:
6x-5>-29
6x-5+5>-29+5
6x>-24
6x/6>-24/6
x>-4
Answer:
The answer is option d) 16/24 = 12/n
Step-by-step explanation:
16 pound roast will feed 24 people
12 pound will feed ?
16 = 24
12 = n
Cross multiply
16 n = 24 . 12
Which can also be written as
16/24 = 12/n
