36.Divide 3x(5x2+3x3+2) – (2x2+8 – x) by (- 2+3x) and check your answer.
Answers
Solution :-
→ Dividend = 3x(5x + 3x³ - 2) - (2x² + 8 - x) = 9x³ + 15x² - 6x - 2x² + x - 8 = 9x³ + 13x² - 5x - 8
→ Divisor = (3x - 2)
so, dividing by long division method we get,
3x-2)9x³ + 13x² - 5x - 8(3x² + (19x/3) + (23/9)
9x³ - 6x²
19x² - 5x
19x² - 38x/3
23x/3 - 8
23x/3 - 46/9
(-26/9)
therefore,
→ Quotient = 3x² + (19x/3) + (23/9)
→ Remainder = (-26/9) .
now, we know that,
→ Dividend = Divisor * Quotient + Remainder .
putting all values we get,
→ 9x³ + 13x² - 5x - 8 = (3x - 2)[3x² + (19x/3) + (23/9)] + (-26/9)
→ 9x³ + 13x² - 5x - 8 = 9x³ + 19x² + (23x/3) - 6x² - (38x/3) - (46/9) - (26/9)
→ 9x³ + 13x² - 5x - 8 = 9x³ + 19x² - 6x² + (23x - 38x)/3 - (46 + 26)/9
→ 9x³ + 13x² - 5x - 8 = 9x³ + 13x² + (-15x/3) - (72/9)
→ 9x³ + 13x² - 5x - 8 = 9x³ + 13x² - 5x - 8
→ LHS = RHS .
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if a^2+ab+b^2=25
b^2+bc+c^2=49
c^2+ca+a^2=64
Then, find the value of
(a+b+c)² - 100 = ...
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