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kari74 [83]
2 years ago
8

if α,β are the roots of the equation x^{2}-3x+2=0 form an equation whose roots are (α+β)² & (α-β)²

Mathematics
1 answer:
GuDViN [60]2 years ago
6 0

<u>Solution</u><u>:</u><u>-</u>

Let's find roots of x² - 3x + 2

=> x² - 3x + 2 = 0.

=> x² - x - 2x + 2 = 0.

=> x ( x - 1 ) -2 ( x - 1) = 0.

=> ( x - 1 ) ( x - 2 ) = 0.

=> x = 2, 1.

Now

  • ( a + ß )² = (2+1)²=3²=9
  • ( a - ß )² = ( 2 - 1 )² = 1² = 1.

So , equⁿ would be ,

=> x² - ( 9 + 1)x + 9×1=0.

<u>=> x² - 10x + 9=0.</u>

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Answer:

The answer to your question is car 1 = 30 gal and car 1 = 20 gal

Step-by-step explanation:

car 1 = a

car 2 = b

Efficiency of car 1 = 35 mi/gal

Efficiency for car 2 = 20 mi/gal

Total distance = 1450

Total gas consumption = 50 gal

Equations

                          35a + 20b = 1450            ------- (I)

                             a   +     b =  50               ------- (II)

Solve by elimination

Multiply equation II by -35

                          35a  + 20b  = 1450

                         -35a  - 35b   = -1750

Simplify

                            0    - 15b    =  -300

Solve for b

                                        b =  -300/-15

Result

                                        b = 20

Substitute b in equation II to find a

                               a +  20  = 50

Solve for a

                               a  = 50 -20

Result

                               a  = 30

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Answer:

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