Math, asked by aduadinan516, 5 months ago

if a+ib = (x+i)square /2x square +1.prove that a square +b square =(x square +1) square /(2x square +1) square


pls help me​

Answers

Answered by abduldudekula55
0

Answer:

a+ib= (x+I)^2/2x^2+1

using (a+b)^2=a^2+b^2+2ab

= (x^2+i^2+2xi)/(2x^2+1)

put i^2= -1,

= (x^2-1)/(2x+1)+i (2x)/(2x^2+1)

comparing real part

a=xsquare-1/2xsquare+1

comparing imaginary p....

b=2x/2xsquare+1

calculating .. a square+b square

a square+b square =( x square-1/2x square+1)Square +(2x/2x Square+1)Square

=(x Square-1) Square+(2x)Square/(2x Square+1) Square

Using (a-b)^2= a square+b square-2an

=(x square)Square+1 square-2(x square)1+4x square/ (2x square+ 1)2

= x^4+1-2x square+4x square/(2x square+2) Square

= x^4+1+2x square/(2x square+1)Square

(x^2) Square+(1 )square+2x square (1)

..' a square + b square =( x Square+1) Square/(2x Square+1 ).

Step-by-step explanation:

a+ib= (x+I)^2/2x^2+1

using (a+b)^2=a^2+b^2+2ab

= (x^2+i^2+2xi)/(2x^2+1)

put i^2= -1,

= (x^2-1)/(2x+1)+i (2x)/(2x^2+1)

comparing real part

a=xsquare-1/2xsquare+1

comparing imaginary p....

b=2x/2xsquare+1

calculating .. a square+b square

a square+b square =( x square-1/2x square+1)Square +(2x/2x Square+1)Square

=(x Square-1) Square+(2x)Square/(2x Square+1) Square

Using (a-b)^2= a square+b square-2an

=(x square)Square+1 square-2(x square)1+4x square/ (2x square+ 1)2

= x^4+1-2x square+4x square/(2x square+2) Square

= x^4+1+2x square/(2x square+1)Square

(x^2) Square+(1 )square+2x square (1)

..' a square + b square =( x Square+1) Square/(2x Square+1 ).

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