If a and b are the rational numbers and 5+2route3/7+4route3=a-broute3,find the values of a and b.
Answers
Answered by
6
Heya !!!
5 + 2✓3 / 7 + 4✓3 = A - B✓3
LHS = 5+ 2✓3/ 7 + 4✓3
Rationalizing the denominator 7 + 4✓3
=> 5 + 2✓3 / 7 + 4✓3 × 7 - 4✓3 / 7 -4✓3
=> ( 5 + 2✓3 ) ( 7 + 4✓3) / ( 7 -4✓3)
=> 5 ( 7 -4✓3) + 2✓3 ( 7 -4✓3) / (7)² - (4✓3)²
=> 35 - 20✓3 + 14✓3 - 24 / 49 -48
=> 35 - 24 - 20✓3 + 14✓3 /1
=> 11 - 6✓3 / 1
=> 11 - 6✓3
Now,
LHS = RHS
11- 6✓3 = A - B✓3
Clearly,
A = 11 and B = 6
HOPE IT WILL HELP YOU...... :-)
5 + 2✓3 / 7 + 4✓3 = A - B✓3
LHS = 5+ 2✓3/ 7 + 4✓3
Rationalizing the denominator 7 + 4✓3
=> 5 + 2✓3 / 7 + 4✓3 × 7 - 4✓3 / 7 -4✓3
=> ( 5 + 2✓3 ) ( 7 + 4✓3) / ( 7 -4✓3)
=> 5 ( 7 -4✓3) + 2✓3 ( 7 -4✓3) / (7)² - (4✓3)²
=> 35 - 20✓3 + 14✓3 - 24 / 49 -48
=> 35 - 24 - 20✓3 + 14✓3 /1
=> 11 - 6✓3 / 1
=> 11 - 6✓3
Now,
LHS = RHS
11- 6✓3 = A - B✓3
Clearly,
A = 11 and B = 6
HOPE IT WILL HELP YOU...... :-)
Similar questions