Find and correct the errors in the following mathematical statements.
1. 4(x–5) = 4x–5
Solution:
Let us take LHS
= 4(x- 5)
= 4x – 20 ≠ 4x – 5 = RHS
Hence, the correct statement is 4(x-5) = 4x–20
2. x(3x+2) = 3x2+2
Solution:
Let us take LHS
= x(3x+2)
= 3x2+2x ≠ 3×2+2 = RHS
Hence, the correct solution is x(3x+2) = 3x2+2x
3. 2x+3y = 5xy
Solution:
Here,
LHS= 2x+3y
RHS = 5xy
Hence, LHS ≠ RHS
The correct statement is 2x+3y = 2x+3 y
4. x+2x+3x = 5x
Solution:
We take LHS:
LHS = x+2x+3x = 6x
Hence, LHS≠ RHS
The correct statement is x+2x+3x = 6x
5. 5y+2y+y–7y = 0
Solution:
We take LHS
LHS = 5y+2y+y–7y = y
LHS ≠ RHS
Hence, the correct statement is 5y+2y+y–7y = y
6. 3x+2x = 5x2
Solution:
We take LHS
LHS = 3x+2x = 5x
LHS ≠ RHS
Hence, the correct statement is 3x+2x = 5x
7. (2x)2+4(2x)+7 = 2×2+8x+7
Solution:
We take LHS
LHS = (2x)2+4(2x)+7
= 4x2+8x+7
LHS ≠ RHS
Hence, the correct statement is (2x)2+4(2x)+7 = 4x2+8x+7
8. (2x)2+5x = 4x+5x = 9x
Solution:
We take LHS
LHS = (2x)2+5x
= 4x2+5x ≠ 9x
LHS ≠ RHS
Hence, the correct statement is(2x)2+5x = 4x2+5x
9. (3x + 2)2 = 3x2+6x+4
Solution:
We take LHS
LHS = (3x+2)2
= (3x)2+22+2x2x3x
= 9x2+4+12x
LHS ≠ RHS
Hence, the correct statement is (3x + 2)2 = 9x2+4+12x
10. Substituting x = – 3 in
(a) x2 + 5x + 4 gives (– 3) 2+5(– 3) +4 = 9+2+4 = 15
Solution:
= (– 3) 2+5(– 3) + 4
= 9–15+4
= – 2.
Hence, this is the correct answer.
(b) x2 – 5x + 4 gives (– 3) 2– 5( – 3)+4 = 9–15+4 = – 2
Solution:
= (–3) 2–5(– 3) +4
= 9+15+4
= 28.
Hence, this is the correct answer
(c) x2 + 5x gives (– 3) 2+5(–3) = – 9–15 = – 24
Solution:
= (– 3) 2+5(–3)
= 9–15
= -6.
Hence, this is the correct answer
11.(y–3)2 = y2–9
Solution:
LHS = (y–3)2
Using identity: (a–b) 2 = a2+b2-2ab
(y – 3)2
= y2+(3)2–2y×3
= y2+9 –6y ≠ y2 – 9
LHS ≠ RHS
The correct statement is (y–3)2 = y2 + 9 – 6y
12. (z+5)2 = z2+25
Solution:
LHS = (z+5)2
Using identity: (a+b)2 = a2+b2+2ab.
(z+5)2 = z2+52+2×5×z = z2+25+10z ≠ z2+25 = RHS
LHS ≠ RHS
The correct statement is (z+5)2 = z2+25+10z
13. (2a+3b) (a–b) = 2a2–3b2
Solution:
LHS = (2a+3b) (a–b)
= 2a(a–b)+3b(a–b)
= 2a2–2ab+3ab–3b2
= 2a2+ab–3b2 ≠ 2a2–3b2
LHS ≠ RHS
The correct statement is (2a +3b)(a –b) = 2a2+ab–3b2
14. (a+4) (a+2) = a2+8
Solution:
LHS = (a+4)(a+2)
= a(a+2)+4(a+2)
= a2+2a+4a+8
= a2+6a+8
LHS ≠ RHS
Hence, the correct statement is (a+4)(a+2) = a2+6a+8
15. (a–4)(a–2) = a2–8
Solution:
LHS = (a–4)(a–2)
= a(a–2)–4(a–2)
= a2–2a–4a+8
= a2–6a+8
LHS ≠ RHS
The correct statement is (a–4)(a–2) = a2–6a+8
16. 3x2/3x2 = 0
Solution:
LHS = 3x2/3x2 = 1
LHS ≠ RHS
The correct statement is 3x2/3x2 = 1
17. (3x2+1)/3x2 = 1 + 1 = 2
Solution:
LHS = (3x2+1)/3x2
= (3x2/3x2)+(1/3x2)
= 1+(1/3x2) ≠ 2
LHS ≠ RHS
The correct statement is (3×2+1)/3×2 = 1+(1/3×2)
18. 3x/(3x+2) = ½
Solution:
LHS = 3x/(3x+2) ≠ 1/2
LHS ≠ RHS
The correct statement is 3x/(3x+2) = 3x/(3x+2)
19. 3/(4x+3) = 1/4x
Solution:
LHS = 3/(4x+3) ≠ 1/4x
LHS ≠ RHS
The correct statement is 3/(4x+3) = 3/(4x+3)
20. (4x+5)/4x = 5
Solution:
LHS = (4x+5)/4x
= 4x/4x + 5/4x
= 1 + 5/4x ≠ 5 = RHS
LHS ≠ RHS
The correct statement is (4x+5)/4x = 1 + (5/4x)
21. (7x + 5)/5 = 7x
Solution:
LHS = (7x+5)/5
= (7x/5)+ 5/5
= (7x/5)+1 ≠ 7x = RHS
LHS ≠ RHS
Hence, the correct statement is (7x+5)/5 = (7x/5) +1
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