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Find the value of a and b √ 7-1/√ 7+1-√ 7+1/√ 7-1=a+b√ 7
4 months ago
Q:
find the value of a and b √ 7-1/√ 7+1-√ 7+1/√ 7-1=a+b√ 7
Accepted Solution
A:
Answer:a=[tex]\frac{2}{3}[/tex],b=[tex]-\frac{2}{3}[/tex]Step-by-step explanation:Original=[tex]\frac{(\sqrt{7} -1)^{2} }{7-1} -\frac{(\sqrt{7} +1)^{2} }{7-1}[/tex]=[tex]\frac{(\sqrt{7} -1)-(\sqrt{7} +1)^{2} }{6}[/tex]=[tex]\frac{(\sqrt{7}-1+\sqrt{7} -1)(\sqrt{7} -1 -\sqrt{7} -1)}{6}[/tex]=[tex]\frac{-4\sqrt{7} +4}{6}[/tex]=[tex]\frac{2}{3} -\frac{2}{3} \sqrt{7}[/tex]Contrast factora+b√ 7=[tex]\frac{2}{3} -\frac{2}{3} \sqrt{7}[/tex]and so a=[tex]\frac{2}{3}[/tex],b=[tex]-\frac{2}{3}[/tex]