Question

a+b = 3
ab = 5/4
Find the value of a and b​

Answer 1

Answer:

$a = 3 \: and \: b = 0$

Step-by-step explanation:

given that,

$a + b = 3 \\ ab = \frac{5}{4}$

a + b = 3

Square it on both sides,

$= (a + b)^{2} = {3}^{2}$

we know that,

$(a + b)^{2} = {a}^{2} + {b}^{2} + 2ab$

therefore,

${a}^{2} + {b }^{2} + 2ab = 9$

substitute ab = 5/4 in the above equation

$= {a}^{2} + {b}^{2} + 2 \times \frac{5}{4} = 9$

${a}^{2} + {b}^{2} + 10 = 9$

therefore,

${a}^{2} + {b }^{2} = 1$

we know that,

${a}^{2} + {b}^{2} = (a - b) {}^{2} + 2ab$

$1 = (a - b) {}^{2} + 10$

$a - b = \sqrt{ - 9}$

$a - b = 3$

now adding equation of

$a + b \: and \: a - b$

$a + b + a - b = 3 + 3$

$2a = 6$

$a = 3$

substitute a in

$a + b$

$3 + b = 3$

$b = 0$

therefore,

$a = 3 \: and \: b = 0$

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