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let a and b be the solutions to 5x^2-11x+4=x^2-7x + 3

 

Find 1/a + 1/b

 May 1, 2022

Best Answer 

 #1
avatar+220 
+2

Pull over terms to the left side:

4x²-4x+1=0

Factor:

(2x-1)²=0

a would be 1/2. b would also be 1/2.

1/a + 1/b would be 4.

 May 1, 2022
 #1
avatar+220 
+2
Best Answer

Pull over terms to the left side:

4x²-4x+1=0

Factor:

(2x-1)²=0

a would be 1/2. b would also be 1/2.

1/a + 1/b would be 4.

WhyamIdoingthis May 1, 2022
 #2
avatar+1366 
+1

Simplify the equation to: \(4x^2-4x+1=0\)

 

We can rewrite \({1 \over a} + {1 \over b} \) as \({b+a} \over {ab}\)

 

Using Vieta's, the sum of the roots (a+b) is \(-b \over a\) and the product (ab) is \(c \over a\)

 

This means that the sum of the roots is \({4 \over 4} = 1\), and that the product of the roots is \(1 \over 4\)

 

Substituting this in, we find that \(\large{{1 \over a} + {1 \over b} = {1 \over {1 \over 4}} = \color{brown}\boxed{4}}\)

 May 1, 2022

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