If 2a+ 2/a =4, what is the value of 2a^2− 2/a^2 ?
2a+2/a=4
a+1/a=2
a^2+1=2a
a^2-2a+1=0
(a-1)^2=0
a=1
2(1^2+(2/(1)^2)=4
thanks
To find the value of 2a^2 − 2/a^2, we need to first simplify 2a + 2/a = 4.
We can start by finding a common denominator:
2a + 2/a = (2a^2 + 2) / a
Now, we can set the equation equal to 4:
(2a^2 + 2) / a = 4
Next, we can cross multiply:
2a^2 + 2 = 4a
Rearranging the equation by subtracting 4a on both sides:
2a^2 - 4a + 2 = 0
To find the value of a, we can use the quadratic formula:
a = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 2, b = -4, and c = 2. Plugging these values into the formula:
a = (-(-4) ± √((-4)^2 - 4(2)(2))) / (2(2))
= (4 ± √(16 - 16)) / 4
= (4 ± √0) / 4
= 4/4
= 1
Therefore, a = 1.
Now, we can substitute the value of a into 2a^2 − 2/a^2:
2(1)^2 - 2/(1)^2
= 2(1) - 2/1
= 2 - 2
= 0
Therefore, the value of 2a^2 − 2/a^2 is 0.
To find the value of 2a^2 - 2/a^2, let's first simplify the equation 2a + 2/a = 4.
Step 1: Get rid of the fraction in the equation by multiplying both sides of the equation by the denominator, which is "a":
2a * a + 2/a * a = 4 * a
2a^2 + 2 = 4a
Step 2: Move all the terms to one side of the equation to make it equal to zero:
2a^2 + 2 - 4a = 0
Step 3: Rearrange the equation in descending order:
2a^2 - 4a + 2 = 0
Step 4: Now, let's find the roots of the quadratic equation using either the quadratic formula or factoring. In this case, let's factorize the equation:
2a^2 - 2a - 2a + 2 = 0
2a(a - 1) - 2(a - 1) = 0
(2a - 2)(a - 1) = 0
Step 5: Set each factor equal to zero and solve for "a":
2a - 2 = 0 or a - 1 = 0
2a = 2 or a = 1
a = 1 or a = 1
Step 6: Now that we have found the value of "a" as 1, we can substitute it into the expression 2a^2 - 2/a^2 to get the final answer:
2(1)^2 - 2/(1)^2
2(1) - 2/1
2 - 2
0
Therefore, the value of 2a^2 - 2/a^2 is 0.