if (2-√5)+(3+2√5)-(4+5)/4=p+q√5 find the value of p and q
Answers
Step-by-step explanation:
\tt{ \implies \: \frac{ (2- \sqrt{ 5 } )+(3+2 \sqrt{ 5 } )-(4+ \sqrt{ 5 } ) }{ 4 } =p+q \sqrt{ 5 }}⟹4(2−5)+(3+25)−(4+5)=p+q5
\tt{ \implies \:2-\sqrt{5}+3+2\sqrt{5}-\left(4+\sqrt{5}\right)=4p+4q\sqrt{5} }⟹2−5+3+25−(4+5)=4p+4q5
\tt{ \implies \:5-\sqrt{5}+2\sqrt{5}-\left(4+\sqrt{5}\right)=4p+4q\sqrt{5} }⟹5−5+25−(4+5)=4p+4q5
\tt{ \implies \:5+\sqrt{5}-\left(4+\sqrt{5}\right)=4p+4q\sqrt{5} }⟹5+5−(4+5)=4p+4q5
\tt{ \implies5+\sqrt{5}-4-\sqrt{5}=4p+4q\sqrt{5} }⟹5+5−4−5=4p+4q5
\tt{ \implies \: 1+\sqrt{5}-\sqrt{5}=4p+4q\sqrt{5} }⟹1+5−5=4p+4q5
\tt{ \implies \: 1=4p+4q\sqrt{5} }⟹1=4p+4q5
\tt{ \implies \: 4p=1-4q\sqrt{5} }⟹4p=1−4q5
\tt{ \implies \:\frac{4p}{4}=\frac{-4\sqrt{5}q+1}{4} }⟹44p=4−45q+1
\tt{ \implies \:p=-\sqrt{5}q+\frac{1}{4} }⟹p=−5q+41
Answer:
Step-by-step explanation:
hope it help you.
thanks
Answer:
Step-by-step explanation:
\tt{ \implies \: \frac{ (2- \sqrt{ 5 } )+(3+2 \sqrt{ 5 } )-(4+ \sqrt{ 5 } ) }{ 4 } =p+q \sqrt{ 5 }}⟹
4
(2−
5
)+(3+2
5
)−(4+
5
)
=p+q
5
\tt{ \implies \:2-\sqrt{5}+3+2\sqrt{5}-\left(4+\sqrt{5}\right)=4p+4q\sqrt{5} }⟹2−
5
+3+2
5
−(4+
5
)=4p+4q
5
\tt{ \implies \:5-\sqrt{5}+2\sqrt{5}-\left(4+\sqrt{5}\right)=4p+4q\sqrt{5} }⟹5−
5
+2
5
−(4+
5
)=4p+4q
5
\tt{ \implies \:5+\sqrt{5}-\left(4+\sqrt{5}\right)=4p+4q\sqrt{5} }⟹5+
5
−(4+
5
)=4p+4q
5
\tt{ \implies5+\sqrt{5}-4-\sqrt{5}=4p+4q\sqrt{5} }⟹5+
5
−4−
5
=4p+4q
5
\tt{ \implies \: 1+\sqrt{5}-\sqrt{5}=4p+4q\sqrt{5} }⟹1+
5
−
5
=4p+4q
5
\tt{ \implies \: 1=4p+4q\sqrt{5} }⟹1=4p+4q
5
\tt{ \implies \: 4p=1-4q\sqrt{5} }⟹4p=1−4q
5
\tt{ \implies \:\frac{4p}{4}=\frac{-4\sqrt{5}q+1}{4} }⟹
4
4p
=
4
−4
5
q+1
\tt{ \implies \:p=-\sqrt{5}q+\frac{1}{4} }⟹p=−
5
q+
4
1
Answer:
Step-by-step explanation:
hope it help you.
thanks