express 2x^2 +3x+5 as a sum or diffrence of two squares


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Question Number 123315 by aurpeyz last updated on 24/Nov/20

$e x p r e s s 2 x^{2} + 3 x + 5 a s a s u m o r$ $d i f f r e n c e o f t w o s q u a r e s$
Commented by mr W last updated on 24/Nov/20

$a n s w e r i n Q 123143 n o t g o o d f o r y o u ?$
	Answered by mathmax by abdo last updated on 24/Nov/20
	$2x^2 +3x+5 =2{x^2 +(3/2)x+(5/2)} =2{x^2 +2.(3/4)x +(9/(16))+(5/2)−(9/(16))} =2{(x+(3/4))^2 +((31)/(16))} =2(x+(3/4))^2 +((31)/8) =((√2)(x+(3/4)))^2 +((√((31)/8)))^2$
	${2 x}^{2} + 3 x + 5 = 2 {x^{2} + \frac{3}{2} x + \frac{5}{2}}$ $= 2 {x^{2} + 2 . \frac{3}{4} x + \frac{9}{16} + \frac{5}{2} - \frac{9}{16}} = 2 {{(x + \frac{3}{4})}^{2} + \frac{31}{16}}$ $= 2 {(x + \frac{3}{4})}^{2} + \frac{31}{8} = {(\sqrt{2} (x + \frac{3}{4}))}^{2} + {(\sqrt{\frac{31}{8}})}^{2}$
	Commented by aurpeyz last updated on 25/Nov/20

	$t h a n k y o u e v e r y o n e$
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