Answer:
hope I will and you do to
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:
r = 31.85 in or 100/π
Step-by-step explanation:
area = πd
200 = 3.14d
d = 63.69
r = 1/2d
r = 31.85 in
Answer:
x=-5/7
Step-by-step explanation:
If 21 is added to (+ 21) a number (x) the result (=) is 40 less than (- 40) twice the number (2x)
x + 21 = 2x - 40 Add 40 to both sides
x + 61 = 2x Subtract x from both sides
61 = x Switch the sides to make it easier to read
x = 61
