Question

p(X) = 3x^2-8x+4 find α^2/β^2 + β^2/α^2

Answer 1

★ Ello ★

here is your answer !!


look this attachment :-


hope it helps you dear !!


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at second. page :-



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Answer 2

HELLO DEAR,


GIVEN THAT:-

3x² - 8x + 4

where,

a = 3

b = (-8)

c = 4


now,


(alpha + beta) = -b/a = -(-8)/3 = 8/3----------(1)

(alpha × beta) = c/a = 4/3

now,

we know that:-

(a - b)² = (a + b)² - 4ab

use this formula here,

(alpha - beta)² = (alpha + beta)² - 4alpha × beta

(alpha - beta)² = (8/3)² - 4(4/3)

(alpha - beta)² = 64/9 - 16/3

(alpha - beta)² = (64 - 48)/9

(alpha - beta)² = 16/9

(alpha - beta) = 4/3----------(2)



from-----(1) & -----(2)

alpha + beta = 8/3
alpha - beta = 4/3
----------------------------
2alpha = 1/3(8 + 4)

alpha = 12/6

alpha = 2 --[put in --(1)]


we get,

alpha + beta = 8/3

2 + beta = 8/3

beta = 8/3 - 2

beta = (8 - 6)/3

beta = 2/3



NOW,


(alpha ²)/(beta²) + (beta²)/(alpha ²)


(alpha⁴ + beta ⁴)/ (alpha² * beta²)

= (16 + 16/81) / (4 * 4/9)

= [(1296 + 16)/81] / (16/9)

= (1312)/81 / 16/9

= 1312/144

= 164/18


I HOPE ITS HELP YOU DEAR,
THANKS