please give me some questions for linear equations in one variable.......
Answers
Answer:
Question 1: Add: a + b + ab ; b – c + bc and c + a + ac
Solution: We have :
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Thus, the sum of the given expressions is 2a + 2b + ab + bc + ca.
Question 2: Verify the identity (x + a)( x + b) = x2 + (a + b)x + ab for a = 2, b = 3 and x = 4,
Solution: We have
(x + a)(x + b) = x2 + (a + b)x + ab
Puting x = 2, b = 3 and x = 4, we have
LHS = (x + a)(x + b)
= (4 + 2)(4 + 3)
= 6 * 7 = 42
RHS = x2 + (a + b)x + ab
= (4)2 + (2 + 3)4 + (2 * 3)
= 16 + 5 * 4 + 6
= 16 + 20 + 6 = 42
i.e. LHS = RHS
Thus, the given identity is true for the given values.
Question 3: Using a suitable identity to get the product: Extra Questions- Comparing Quantities
Solution: Using the identity (a – b)2 = a2 – 2ab + b2, we have
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Question 4: The length and breadth of a rectangle are 3x2 – 2 and 2x + 5 respectively. Find its area.
Solution: Here,
Length = 3x2 – 2
Breadth = 2x + 5
∴ Area = (Length) * (Breadth)
= (3x2 – 2) * (2x + 5)
= 3x2(2x + 5) + (–2)(2x + 5)
= (3x2 * 2x) + (5 * 3x2) + [(–2) * 2x + (–2) * 5]
= 6x3 + 15x2 + (–4x) + (–10) = 6x3 + 15x2 – 4x – 10
Thus, the required area of the rectangle is 6x3 + 15x2 – 4x – 10 sq. units.
Question 5: Find the volume of cuboid whose dimensions are (x2 – 2); (2x + 2) and (x – 1).
Solution: ∵ Volume of a cuboid = Length * Breadth * Height
Extra Questions- Comparing Quantities
Extra Questions- Comparing Quantities