Answer:
for ur satisfaction (2) 2^10
Step-by-step explanation:
Let a=1+2009√2 . Find the value of (a3−503a−500)5 i hope ur right que is this!!
It should be [tex]\text{$(a^{3}-503a-500)^{3}$}[/tex].
[tex]\;[/tex]
[tex]\text{$\bigg(a=\dfrac{1+\sqrt{2009}}{2}\bigg)$}[/tex]
For integer coefficients, we square both sides.
[tex]\text{$2a=1+\sqrt{2009}$}[/tex]
[tex]\text{$(2a-1)^{2}=2009$}[/tex]
[tex]\text{$4a^{2}-4a+1=2009$}[/tex]
[tex]\text{$4a^{2}=4a+2008$}[/tex]
[tex]\text{$\therefore a^{2}=a+502$}[/tex]
LHS
[tex]\text{$=(a^{3}-503a-500)^{10}$}[/tex]
[tex]\text{$=(a^{2+1}-503a-500)^{10}$}[/tex]
[tex]\text{$=(a^{2}+502a-503a-500)^{10}$}[/tex]
[tex]\text{$=(a^{2}-a-500)^{10}$}[/tex]
Now we substitute the value of [tex]\text{$a^{2}$}[/tex] into the expression.
[tex]\text{$=(a+502-a-500)^{10}$}[/tex]
[tex]\text{$=2^{10}$}[/tex]
RHS
Option 2 is the correct choice.
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Answers & Comments
Answer:
for ur satisfaction (2) 2^10
Step-by-step explanation:
Let a=1+2009√2 . Find the value of (a3−503a−500)5 i hope ur right que is this!!
Verified answer
Correct Question
It should be [tex]\text{$(a^{3}-503a-500)^{3}$}[/tex].
[tex]\;[/tex]
Solution
[tex]\text{$\bigg(a=\dfrac{1+\sqrt{2009}}{2}\bigg)$}[/tex]
[tex]\;[/tex]
For integer coefficients, we square both sides.
[tex]\text{$2a=1+\sqrt{2009}$}[/tex]
[tex]\text{$(2a-1)^{2}=2009$}[/tex]
[tex]\text{$4a^{2}-4a+1=2009$}[/tex]
[tex]\text{$4a^{2}=4a+2008$}[/tex]
[tex]\text{$\therefore a^{2}=a+502$}[/tex]
[tex]\;[/tex]
LHS
[tex]\text{$=(a^{3}-503a-500)^{10}$}[/tex]
[tex]\text{$=(a^{2+1}-503a-500)^{10}$}[/tex]
[tex]\text{$=(a^{2}+502a-503a-500)^{10}$}[/tex]
[tex]\text{$=(a^{2}-a-500)^{10}$}[/tex]
Now we substitute the value of [tex]\text{$a^{2}$}[/tex] into the expression.
[tex]\text{$=(a+502-a-500)^{10}$}[/tex]
[tex]\text{$=2^{10}$}[/tex]
[tex]\;[/tex]
RHS
[tex]\text{$=2^{10}$}[/tex]
[tex]\;[/tex]
Option 2 is the correct choice.