7+3 root 5by 3+ root 5 minus 7-3 root 5 by 3- root 5 = a+ root 5 b find the value of a and b
Answers
Answer:
a = 0
b = 1
Step-by-step explanation:
7+3 root 5by 3+ root 5 minus 7-3 root 5 by 3- root 5 = a+ root 5 b find the value of a and b
(7 + 3√5)/(3 + √5) - (7 - 3√5)/(3 - √5) = a + b√5
LHS
= (7 + 3√5)/(3 + √5) - (7 - 3√5)/(3 - √5)
= ( (7 + 3√5)(3 - √5) - (7 - 3√5)(3 + √5) ) / ( 3² - √5²)
= (21 + 2√5 - 15 - (21 -2√5 -15) ) / ( 9 - 5)
= 4√5 / 4
= √5
= 0 + 1 *√5
Comparing with RHS
a + b√5
a = 0
b = 1
Answer:
a = 0 ; b = 1 ;
Explanation:
(7+3√5 / 3+√5 ) - (7-3√5 / 3-√5 ) = (7+3√5 )(3-√5) - (7-3√5 )(3+√5)
/ (3+√5)
= (21-7√5 +9√5 -15) - (21+7√5 -9√5 -15) / 3²-(√5)²
= 21-7√5 +9√5 -15 - 21-7√5 +9√5 +15) / 9-5
= 4√5 / 4
= √5
(7+3√5 / 3+√5 ) - (7-3√5 / 3-√5 ) = a + √5 *b
Therefore,
√5 = a + √5 *b
⇒ 0+ √5*1 = a + √5 *b
⇒ a = 0 ; b = 1 ;