Question

Pls solve it fast find 3/4(alphasquare -beta square ​

Answer 1

$\huge \underline \bold \green{QUESTION}:$

$if \: \alpha \: and \: \beta \: ar e\: the \: roots \: of \: equation \\ \: {x}^{2} - 5x + 6 \: \: then \: find \: \frac{3}{4} ( { \alpha }^{2} - { \beta }^{2} )$

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$\huge \underline \bold \red{SOLUTION}:$

${x}^{2} - 5x + 6 = 0 \\ = > {x}^{2} - 2x - 3x + 6 = 0 \\ = > x(x - 2) - 3(x - 2) = 0 \\ = > (x - 2)(x - 3) = 0 \\ = > \alpha = 3 \\ = > \beta = 2 \\ now \: the \: value \: of \: \\ \frac{3}{4} ( { \alpha }^{2} - { \beta }^{2} ) \\ = > \frac{3}{4} ( {3}^{2} - {2}^{2} ) \\ = > \frac{3}{4} (9 - 4) \\ = > \frac{3}{4} (5) \\ = > \frac{15}{4}$

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$\underline\bold \red{final \: answer}$

$\huge = > \frac{15}{4}$

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Answer 2

Answer:

15/4

Step-by-step explanation:

Given, a and b are zeroes of given equation x^2-5x+6=0

(I have taken alpha and beta as a and b)

then on solving equation we get

(x-2)(x-3)=0

that means a=3 and b=2

Now, 3/4(a^2-b^2)

=3/4[(9-4)

= 5×3/4 = 15/4

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