Question

If 3+√7/3-4√7= a+b√7 where a and b are rational numbers, find the values of a and b​

Answer 1

Answer:

=(a+b)7,    cross−multiply,3+7=(3−47)∗[(a+b)7]

\begin{gathered}3 + \sqrt7 = (3a+3b)\sqrt7-4(a+b)\sqrt7*\sqrt7 \\ \\ 3 + \sqrt7 = (3a+3b) \sqrt{7} - (4a+4b)*7 \\ \\ 3+\sqrt7 = -(28a+28b) + (3a+3b)\sqrt7 \\ \\ equate\ rational\ and\ irrational\ parts \\ \\ 28a+28b = -3,\ \ \ \ and\ \ \ 3a +3b = 1 \\ \\ There\ is\ inconsistency\ as\ a+b=-3/28\ according\ to\ 1st\ equation \\ \\ a+b=1/3\ according\ to\ 2nd\ equation \\ \\ there\ is\ no\ solution\end{gathered}3+7=(3a+3b)7−4(a+b)7∗73+7=(3a+3b)7−(4a+4b)∗73+7=−(28a+28b)+(3a+3b)7equate rational and irrational parts28a+28b=−3,    and   3a+3b=1There is inconsistency as a+b=−3/28 according to 1st equationa+b=1/3 according to 2nd equationthere is no solution

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\begin{gathered}If\ RHS\ =\ a + b\ \sqrt7,\ \ then, \\ \\ 3a-28b=3\ \ \ and\ 3b-4a=1 \\ \\ Solving\ we\ get \\ \\ b = -15/103\ \ and\ \ \ a = -37/103\end{gathered}If RHS = a+b 7,  then,3a−28b=3   and 3b−4a=1Solving we getb=−15/103  and   a=−37/103.....hope it helps....mark me as brainlist

Answer 2

Answer:

here's ur answer

pls mark brainliest