Question

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Answer 1

Answer:

Given quadratic equation,

2x² - 5x + 2 = 0.

By splitting the middle term,

➜ 2x² - 4x - x + 2 = 0

➜ 2x(x - 2) - 1(x - 2) = 0

➜ (2x - 1)(x - 2) = 0

➜ x = 1/2 and 2.

Now, alpha = 2 and beta = 1/2.

Here, (alpha > beta), that is why we took alpha as 2 and beta as 1/2.

So, (alpha - 1)^(beta - 1)

Solving, (2 - 1)^(1/2 - 1)

➜ (1)^((1-2)/2)

➜ (1)^(-1/2)

➜ √1

➜ 1

Final Answer = 1.

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Answer 2

AnswEr :

Value of given expression is 1

Explanation :

Given Equation,

$\sf \: 2 {x}^{2} - 5x +2 = 0$

Splitting the middle term,

$\longrightarrow \: \sf \: {2x}^{2} - 4x - x + 2 = 0 \\ \\ \longrightarrow \: \sf \: ( x - 2)(2x - 1) = 0 \\ \\ \longrightarrow \: \boxed{ \boxed{ \sf x = 2 \: or \: \dfrac{1}{2} }}$

Thus,

$\sf \: \alpha = 2 \: and \: \beta = \dfrac{1}{2}$

Now,

$\sf ( \alpha - 1) {}^{ \beta - 1} \\ \\ \longrightarrow \: \sf \: ( 2 - 1) {}^{ - \frac{1}{2} + 1} \\ \\ \longrightarrow \sf (1)^({\frac{1}{2}}) \\ \\ \large{ \longrightarrow \: 1}$