Question

7-4√3/7+4√3=a+b√3 what is ans

Answer 1

Answer:

(7-4√3)/(7+4√3)*(7-4√3)/(7-4√3)= a+b√3

(7)²+2(7)(4√3)+(4√3)²/(7)²-(4√3)²= a+b√3

49+56√3+48/49-48= a+b√3

97+56√3/1=a+b√3

so, a= 97&

b√3=56√3

hope this helps you!!!plz mark me as brainliest.

Answer 2

$\large \rm{ \frac{7 - 4 \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3} }$

$\sf{rationalise \: the \: denominator}$

$\implies \large \rm{ \frac{7 - 4 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = a + b \sqrt{3} }$

$\implies \large \rm{ \frac{{(7 - 4 \sqrt{3})}^{2} }{ {7}^{2} - {(4 \sqrt{3})}^{2} } = a + b \sqrt{3} }$

$\star \: \sf{note:{(4 \sqrt{3})}^{2} = {4}^{2} \times { \sqrt{3} }^{2} } \\ \rightarrow16 \times 3 = 48 \\ \sf{expand \: {(7 - 4 \sqrt{3} )}^{2} } \: using \: formula \: {(a - b)}^{2}$

$\implies \large \rm{ \frac{{{7}^{2} - 2(7)(4 \sqrt{3} ) + (4 \sqrt{3})}^{2} }{ 49 - 48 } = a + b \sqrt{3} }$

$\implies \large \rm{ \frac{49- 56\sqrt{3} + 48 }{ 49 - 48 } = a + b \sqrt{3} }$

$\implies \large \rm{ 97- 56\sqrt{3} = a + b \sqrt{3} }$

$\large \star \: { \rm{a = 97}}$

$\large \star \: { \rm{b = 56 }}$