a=root 8 + 2.
b=root 8 - 2
t=a*2 - b *2.
work out the value of t.give your answer in the form c root 2 where c is an integer.
√8 = √ ( 4 • 2 ) = √4 • √ 2 = 2 √2
a = √8 + 2 = 2√2 + 2
b = √8 - 2 = 2√2 - 2
a^2 - b^2 = ( a + b ) ( a - b ) =
( 2 √2 + 2 + 2 √2 - 2 ) • [ 2 √2 + 2 - ( 2 √2 - 2 ) ] =
+
( 2√2 + 2 √2 ) • ( 2 √2 + 2 - 2 √2 + 2 ) =
4√2 • 4 = 16 √2
( 2 √2 + 2 + 2 √2 - 2 ) • [ 2 √2 + 2 - ( 2 √2 - 2 ) ] =
( 2√2 + 2 √2 ) • ( 2 √2 + 2 - 2 √2 + 2 ) =
4√2 • 4 = 16 √2
To find the value of t, we can first simplify the expressions for a and b, and then substitute them into the expression for t.
Given:
a = √(8 + 2)
b = √(8 - 2)
Step 1: Simplify expressions for a and b
a = √10
b = √6
Step 2: Substitute into the expression for t
t = a*2 - b*2
= 2√10 - 2√6
Step 3: Rationalize the denominator
To rationalize the denominator, we multiply the expression by the conjugate of the denominator.
t = (2√10 - 2√6) * (√2 + √2)
= 2√20 + 2√20 - 2√12 - 2√12
= 4√5 - 4√3
Therefore, the value of t is 4√5 - 4√3, in the form c√2 where c is an integer.
To work out the value of t, we need to substitute the given values of a and b into the expression t = a * 2 - b * 2 and simplify.
First, let's find the values of a and b.
a = √(8 + 2)
To simplify this, we need to find the square root of 8 + 2.
8 + 2 = 10
So, a = √10.
b = √(8 - 2)
To simplify this, we need to find the square root of 8 - 2.
8 - 2 = 6
So, b = √6.
Now, let's substitute these values into the expression t = a * 2 - b * 2.
t = (√10) * 2 - (√6) * 2
To simplify this, we can factor out the common factor of 2.
t = 2(√10 - √6)
Therefore, the value of t is 2(√10 - √6).