Question-49147

Question Number 49147 by behi83417@gmail.com last updated on 03/Dec/18

Answered by tanmay.chaudhury50@gmail.com last updated on 03/Dec/18

a b - a d + c d - b c = 0

a (b - d) - c (b - d) = 0

(a - c) (b - d) = 0

e i t h e r a = c o r b = d

l e t a = c

a^{2} + d^{2} = c^{2} + d^{2} s o b = d

h e n c a = c b = d

a + b + c + d = 1

2 a + 2 b = 1 a + b = \frac{1}{2}

a c + b d = 1

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

a^{2} + {(\frac{1}{2} - a)}^{2} = 1 [a + b = \frac{1}{2}]

a^{2} + \frac{1}{4} - a + a^{2} = 1

8 a^{2} - 4 a + 1 = 4

8 a^{2} - 4 a - 3 = 0

a = \frac{4 \pm \sqrt{16 + 96}}{16} = \frac{4 \pm \sqrt{112}}{16} = \frac{4 \pm 4 \sqrt{7}}{16}

a = \frac{1 \pm \sqrt{7}}{4} c = \frac{1 \pm \sqrt{7}}{4}

b = \frac{1}{2} - (a)

b = \frac{1}{2} - (\frac{1 \pm \sqrt{7}}{4}) = \frac{2 - (1 \pm \sqrt{7}}{4}) = \frac{2 - 1 - \sqrt{7}}{4} = \frac{1 - \sqrt{7}}{4}

d = \frac{1 - \sqrt{7}}{4}

b = \frac{2 - 1 + \sqrt{7}}{4} = \frac{1 + \sqrt{7}}{4} = d

s o a = \frac{1 \pm \sqrt{7}}{4}

b = (\frac{1 - \sqrt{7}}{4} a n d \frac{1 + \sqrt{7}}{4})

c = (\frac{1 \pm \sqrt{7}}{4})

d = (\frac{1 - \sqrt{7}}{4} a n d \frac{1 + \sqrt{7}}{4}) \dots p l s c h e c k \dots

Commented by behi83417@gmail.com last updated on 03/Dec/18

t h a n k y o u s o m u c h s i r t a n m a y .

n i c e q u e s t i o n a n d b e a u t i f u l s o l u t i o n!

Commented by tanmay.chaudhury50@gmail.com last updated on 04/Dec/18

t h a n k y o u s i r . .