determine a and b if root 7+root 5/root7-root5 -root7-root5/root7+root5 =a+root 35b
Answers
value of a = 0 and b = 2
your question is .... (√7 + √5)/(√7 - √5) - (√7 - √5)/(√7 + √5) = a + √35 b
then we are to find out values of a and b.
rationalize each part of LHS.
(√7 + √5)/(√7 - √5) = (√7 + √5) × √(7 + √5)/(√7 - √5) × (√7 + √5)
= (√7 + √5)²/(√7² - √5²)
= (√7² + √5² + 2√7.√5)/(7 - 5)
= (7 + 5 + 2√35)/(2)
= (12 + 2√35)/2
= 6 + √35
similarly rationalize other part,
(√7 - √5)/(√7 + √5) = (√7 - √5)²/(√7² - √5²)
= (7 + 5 - 2√35)/2
= (6 - √35)
now, (√7 + √5)/(√7 - √5) - (√7 - √5)/(√7 + √5) = a + √35 b
⇒(6 + √35) - (6 - √35) = a + √35 b
⇒0 + 2√35 = a + √35 b
on comparing we get,
a = 0 and b = 2
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Answer:
Locate root 10 on number line
Step-by-step explanation:
Locate root 10 on number line