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# help algebra

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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

#1
+302
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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
+302
+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.

WhyamIdoingthis May 1, 2022
#2
+2532
0

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