Question

 If α and β are the roots of equation 2 x² - 4x + 10 = 0, then the value of 1/(α²β) + 1/(αβ²) is?​

Answer 1

Step-by-step explanation:

Given -

• α and β are roots of equation p(x) = 2x² - 4x + 10 = 0

To Find -

• Value of 1/(α²β) + 1/(αβ²)

Solution -

1/α²β + 1/αβ²

= α + β/α²β²

We know that,

• α + β = -b/a ..... (i)

= α + β = -(-4)/2

= α + β = 2

And

• αβ = c/a ...... (ii)

= αβ = 10/2

= αβ = 5

Squaring both sides -

α²β² = 25

Then,

The value of α + β/α²β² is

= 2/25

Hence,

The value of 1/(α²β) + 1/(αβ²) is 2/25.

Answer 2

hi there !

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Given - a and b are the roots of the equation 2x²+3x+4=0.

So, a+b=(-3/2) and ab=4/2=2

Also, a and b satisfy it. That implies

2a²+3a+4=0 - ( 1 )

And

2b²+3b+4=0 - ( 2 )

Adding equations ( 1 ) and ( 2 ) , we get

2a²+3a+4 + 2b²+3b+4 = 0

2( a² + b² ) + 3( a + b ) + 8 = 0

2( a² + b² ) + 3(-3/2) + 8 = 0

2( a² + b² ) = 9/2 - 8 = - 7/2

( a² + b² ) = -7/4

hope it helps

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