Find the surface area of the triangular prism. The base of the prism is an isosceles triangle.
40 cm, 41 cm, 43 cm, 18 cm
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Secondary School Math 5 points
If alpha and beta are the zeroes of x2-x-4 find out the value of
1) 1/alpha + 1/beta - alpha beta
2) alpha/beta + beta/alpha +2 ( 1/alpha +1/beta) + 3*alpha*beta..
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Ask for details Follow Report by Arohi03 06.05.2018
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Sol : We have quadratic equation x² - x - 4.
Given α and ß are their zeroes.
We know that,
Sum of roots = - ( coefficient of x )/ coefficient of x²
α + ß = - ( - 1 ) / 1
α + ß = 1 / 1 = 1.
Now,
Product of roots = constant term / coefficient of x²
αß = ( - 4 ) / 1
αß = -4.
1. 1/α + 1/ß - αß
ß + α
= ------------- - αß
αß
By substituting the values of ( α + ß ) and ( αß ),
= ( 1 / -4 ) - ( - 4 )
= ( - 1 / 4 ) + 4
- 1 + 16
= ----------------
4
= 15 / 4.
2. α/ß + ß/α + 2 ( 1/α + 1/ß ) + 3αß
α² + ß² + 2ß + 2α
= --------------------------- + 3αß
αß
α² + ß² + 2 ( α+ß )
= ------------------------- + 3αß ----- eq.1
αß
Now ,we don't have the value of ( α² + ß² ), so let's find it ,
( α + ß )² = α² + ß² + 2 αß
By substituting the values of ( α + ß ) and αß in above equation,
( 1 )² = α² + ß² + 2 ( - 4 )
1 = α² + ß² - 8
α² + ß² = 1 + 8
α² + ß² = 9
Now by substituting the values of ( α² + ß² ) ,αß and ( α + ß ) in eq.1,
9 + 2 ( 1 )
= --------------- + 3 ( - 4 )
-4
9 + 2
= -------------- - 12
-4
- 11
= -------------- - 12
4
-11 - 48
= --------------
4
= -59/4.
Answer:
Step-by-step explanation:
So get the height and the three base sides