Question

if√5=2•236 and √6=2•449, find the value of 1+√2/√5+√3 + 1-√2/√5-√3​

Answer 1

Answer:

       √5 - √6 ≈ -0.213

Step-by-step explanation:

The first term is...

$\displaystyle\frac{1+\sqrt2}{\sqrt5+\sqrt3}=\frac{(1+\sqrt2)(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}\\\\=\frac{\sqrt5-\sqrt3+\sqrt{10}-\sqrt6}{(\sqrt5)^2-(\sqrt3)^2}\\\\=\tfrac12(\sqrt5-\sqrt3+\sqrt{10}-\sqrt6)$

The second term is...

$\displaystyle\frac{1-\sqrt2}{\sqrt5-\sqrt3}=\frac{(1-\sqrt2)(\sqrt5+\sqrt3)}{(\sqrt5-\sqrt3)(\sqrt5+\sqrt3)}\\\\=\frac{\sqrt5+\sqrt3-\sqrt{10}-\sqrt6}{(\sqrt5)^2-(\sqrt3)^2}\\\\=\tfrac12(\sqrt5+\sqrt3-\sqrt{10}-\sqrt6)$

Adding the two terms gives

½(√5-√3+√10-√6) + ½(√5+√3-√10-√6)

= √5 - √6

≈ 2.236 - 2.449

= -0.213

Hope this helps!

Answer 2

Answer:

after solving equation we get. -0.213