Question

if a^2 + b^2 = 29 and ab = 2 find the value of a^4 + b^4​

Answer 1

Step-by-step explanation:

$(a - b) ^ 2 = a ^ 2 + b ^ 2 - 2ab \:$

$=29-2 \times 2$

$=29-4 \\ =25=(a-b)^2 \:$

$therefore, \: a - b = \sqrt{25} = 5$

So answer is 5

Answer 2

$( {a}^{2} + {b}^{2} ) = 29$

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

$= \frac{{a}^{2} + {b}^{2} + 2ab + {a}^{2} + {b}^{2} - 2ab}{2}$

$= \frac{{a}^{2} + {b}^{2} + {a}^{2} + {b}^{2} }{2}$

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

$ab = 4$

$ab = \frac{{a}^{4} + {b}^{4} }{2}$

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

${a}^{4} + {b}^{4} = 8$