Question

4+√5/4-√5+4-√5/4+√5=a+b√5.find the value of a and b.
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Answer 1

${\underline{\underline{\huge{\mathfrak{\green{Answer:-}}}}}}$

Hey Mate!!

$\frac{4+\sqrt{5} }{4-\sqrt{5}} +\frac{4-\sqrt{5} }{4+\sqrt{5}}} \\\\=>\frac{(4+\sqrt{5}) ^{2} }{(4-\sqrt{5})(4+\sqrt{5}) }+ \frac{(4-\sqrt{5}) ^{2} }{(4+\sqrt{5})(4-\sqrt{5}) }\\\\=>\frac{4^{2}+(\sqrt{5})^{2} +2 \times 4 \times \sqrt{5}}{4^{2}-(\sqrt{5})^{2} } +\frac{4^{2}+(\sqrt{5})^{2} -2 \times 4 \times \sqrt{5}}{4^{2}-(\sqrt{5})^{2} } \\\\=> \frac{16+5+8\sqrt{5}}{16-5} +\frac{16+5-8\sqrt{5}}{16-5} \\\\=> \frac{21+8\sqrt{5}}{11} +\frac{21-8\sqrt{5}}{11}\\\\=>\frac{21+8\sqrt{5}+21-8\sqrt{5}}{11}\\\\=>\frac{42}{11}=a+b\sqrt{5}\\\\=>a=\frac{42}{11}, b=0$