If a = root3 - root2/ root3 + root2 and b = root3 + root2/ root3 - root2, find the value of a^2 + b^2- 5ab
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Answer:
Answer= 93
Step-by-step explanation:
A = (√3-√2)/(√3+√2)
=(√3-√2)/(√3+√2)× (√3-√2)/(√3-√2) [ rationalizing it]
=(√3 -√2)²/1 = (√3 -√2)²
= 5- 2√6
B = (√3+√2)/(√3-√2)×(√3+√2)/(√3+√2) [ rationalizing it]
= (√3+√2)²/1 =(√3+√2)²
= 5+2√6
Now,
a²+b² - 5ab = (5-2√6)² + (5+2√6)² - 5(5-2√6)(5+2√6)
=25 +24 -20√6 +25 +24 + 20√6 - 5(25-24)
=98 -5
= 93 (Ans:)
Hope it helped..
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