prefer attachment...for 2 QuesTiOns..
Answers
Answer:
Answer 1)
→ (3 + 5/x)(9 - 15/x + 25/x²) = 3
→ (3 + 5/x){3² - 3 * (5/x) + (5/x)²} = 3
comparing with :-
- (a + b)(a² - ab + b²) = a³ + b³
→ (3)³ + (5/x)³ = 3
→ 27 + (125/x³) = 3
→ (125/x³) = 3 - 27
→ 125 = (-24)x³
→ x³ = (-125/24)
Now,
→ (3 - 5/x)(9 + 15/x + 25/x²)
→ (3 - 5/x){3² + 3 * (5/x) + (5/x)²}
comparing with :-
- (a - b)(a² + ab + b²) = a³ - b³
→ (3)³ - (5/x)³
→ 27 - (125/x³)
Putting value of x³ Now,
→ 27 - {125/(-125/24)}
→ 27 - (-125 * 24) / 125
→ 27 - (-24)
→ 27 + 24
→ 51 (Ans.)
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Answer 2 :-
→ Length of Rectangular Plot = (4x + 3) units
→ Breadth of Rectangular Plot = (2x - 3) units
→ Area of Rectangular Plot = Length * Breadth
→ Area = (4x + 3)(2x - 3) = 8x² - 12x + 6x - 9 = (8x² - 6x - 9) units².
Now,
→ Side of first Square - shaped room = (x + 1) units
→ Area of Room = (side)²
→ Area = (x + 1)² = (x² + 2x + 1) units².
Similarly,
→ Side of second Square - shaped room = (x - 1) units
→ Area of Room = (side)²
→ Area = (x - 1)² = (x² - 2x + 1) units².
Therefore,
→ Area of Remaining Part of the rectangular Plot = Area of Complete rectangular plot - ( Area of first room + Area of second room) .
→ Required Area = (8x² - 6x - 9) - { (x² + 2x + 1) + (x² - 2x + 1) }
→ Required Area = (8x² - 6x - 9) - (2x² + 2)
→ Required Area = 8x² - 6x - 9 - 2x² - 2
→ Required Area = (6x² - 6x - 11) units². (Ans.)