Question-11813

Question Number 11813 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Apr/17

Commented by mrW1 last updated on 01/Apr/17

d e p e n d i n g o n t h e v a l u e s o f a a n d b,

t h e r e a r e 5 c a s e s :

1) n o s o l u t i o n

2) o n e s o l u t i o n

3) t w o s o l u t i o n s

4) t h r e e s o l u t i o n s

5) f o u r s o l u t i o n s

Commented by mrW1 last updated on 01/Apr/17

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Apr/17

t h a n k y o u v e r y m u c h f o r y o u r a n s w e r .

a a n d b, a r e \in N

Answered by sma3l2996 last updated on 01/Apr/17

x = a - y^{2}

{(a - y^{2})}^{2} + y^{2} = b

a^{2} + y^{4} - 2 {a y}^{2} + y^{2} = b

y^{4} - (2 a - 1) y^{2} = b - a^{2}

y^{4} - \frac{(2 a - 1) \times 2}{2} y^{2} + {(\frac{2 a - 1}{2})}^{2} = b - a^{2} + {(\frac{2 a - 1}{2})}^{2}

{(y^{2} - \frac{2 a - 1}{2})}^{2} = b - a^{2} + a^{2} - a + \frac{1}{4} = \frac{4 (b - a) + 1}{4}

y^{2} = \underline{+} \frac{\sqrt{4 (b - a) + 1}}{2} + \frac{2 a - 1}{2}

y = \underline{+} \sqrt{\frac{\underline{+} \sqrt{4 (b - a) + 1} + 2 a - 1}{2}}

x = a - y^{2} = \underline{+} \frac{\sqrt{4 (b - a) + 1} + 2 a - 1}{2} + a

Commented by mrW1 last updated on 01/Apr/17

l i n e 2 s h o u l d b e :

{(a - y^{2})}^{2} + y = b

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Apr/17

t h a n k y o u f o r a n s w e r . b u t a s m r W 1,

p i o n t e d : t h e r i s a l i t t l e m i s t a k e i n

You can't use 'macro parameter character #' in math mode

Commented by sma3l2996 last updated on 01/Apr/17

y e s y o u a l r i g h t