Question

please answer the 26 and 27 questions

Answer 1

26. given, a-b√6=(√2+√3)/(3√2 - 2√3)
=>a-b√6=(√2+√3)(3√2 + 2√3)/{(3√2 +2√3)(3√2 - 2√3)}
=>a-b√6=(√2+√3)(3√2 + 2√3)/(9×2-4×3)
=>a-b√6=(12+2√6+3√6)/(18-12)
=>a-b√6=(12+2√6+3√6)/6
=>6a-6b√6=12+2√6+3√6
=>6a-12=6b√6+2√6+3√6
=>6(a-2)=(√6)(6b+5)
=>36(a-2)²=6(6b+5)²
=>36a²-144a+144=6(36b²+60b+25)
=>36a²-144a+144=216b²+360b+150
=>36a²-216b²-360b-144a-6=0
=>6a²-36b²-60b-24a-1=0

27. x={(√(2p+3q))-(√(2p-3q))}/{(√(2p+3q))+(√(2p-3q))}
=>x={(√(2p+3q))-(√(2p-3q))}²/{(√(2p+3q))+(√(2p-3q))}{(√(2p+3q))-(√(2p-3q))}
=>x={(√(2p+3q))-(√(2p-3q))}²/(2p+3q-2p+3q)
=>x={(√(2p+3q))-(√(2p-3q))}²/6q
=>x={2p+3q+2p-3q-2(√(6q))}/6q
=>x={4p-2(√(6q))}/6q
=>x²={4p-2(√(6q))}²/36q²
Now let's put x and x²s value in the given polynomial.
3qx²-4px+3q
= 3q×{4p-2(√(6q))}²/36q² -4p×{4p-2(√(6q))}/6q +3q
={16p²+24q-16(√(6q))}/12q -4p×{2p-(√(6q))}/3q +3q
[and do some basic algebra to simply it. feeling a bit lazy you know. :3]