Question

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prefer attachment...for 2 QuesTiOns..​

Answer 1

Answer:

$length \: of \: plot = 4x + 3 \\ breadth \: of \: plot = 2x - 3 \\ so \: area \: = l \times b \\ =( 4x + 3) \times (2x - 3) \\ from \: here \: we \: get \: area \: = 2x { }^{2} - x + 4 \\ \\ and \: area \: of \: small \: field \: by \: same \: method \: will \: be \: 5x { }^{2} - 8x \\ so \: area \: of \: remaining \\ portion \: will \: be \: 56cm {}^{2} \:$

Answer 2

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.)

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