Question

a+b=12 and ab= 14 find the value of a and b

Answer 1

Answer: If b=6+5√2 ; a=-6+5√2

If b=6-5√2 ; a = -(6+5√2)

Answer 2

$\bigstar \: \: given \: data \: is \: below \\ \\ \: \: \: a + b = 12......equation(1) \\ \\ \: \: \: ab = 14........equation(2) \\ \\ \: \: \: = > a + b = 12 \\ \\ \: \: \: = > a = 12 - b.....equation \: (3) \\ \\ \bigstar \: equation(3) \: value \: put \: in \: equation(2) \\ \\ \: \: \: = > ab = 14 \\ \\ \: \: \: = > (12 - b)b = 14 \\ \\ \: \: \: = > 12b - {b}^{2} = 14 \\ \\ \: \: \: = > {b}^{2} - 12b + 14 = 0 \\ \\ \: \: \: \: \: \: \: \: \: \delta = { (- 12)}^{2} - 4(1)(14) \\ \\ \: \: \: \: \: \: \: \: \: \delta = 144 - 56 = 88 \\ \\ \: \: \: \: \: \: \: \: \: b \: = \frac{ - ( - 12) \pm \sqrt{ \delta} }{2(1)} \\ \\ \: \: \: \: \: \: \: \: \: b = \frac{12 \pm \sqrt{88} }{2} \\ \\ \: \: \: \: \: \: \: \: \: b = 6 + \frac{ \sqrt{4 \times 22} }{2} \: \: \: \: \: \: \: or \: \: b = 6 + \frac{ \sqrt{4 \times 22} }{2} \\ \\ \: \: \: \: \: \: \: \: \: b = 6 \pm \frac{2 \sqrt{22} }{2 } \\ \\ \: \: \: \: \: \: \: \: \: b = 6 + \sqrt{22 } \: \: \: or \: \: 6 - \sqrt{22} \\ \\ \\ \: \: \: \: when \\ \: \: \: \: \: \: \: b \: = 6 + \sqrt{22} \: \: \: then \: \: a = 6 - \sqrt{22} \\ \\ \: \: \: \: \: \: \: b = 6 - \sqrt{22} \: \: \: then \: \: \: a = 6 + \sqrt{22} \:$