Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1 बीजगणितीय सर्वसमिकाऐं

Ex 4.1 Algebraic Identities अतिलघु उत्तरीय प्रश्न (Very Short Answer Type Questions)

प्रश्न 1.
([latex]\sqrt{5} a+\sqrt{6} b[/latex]) का वर्ग ज्ञात कीजिए।
हलः
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

प्रश्न 2.
(x + 4)(x + 10) का मान ज्ञात कीजिए। [NCERT]
हलः
(x + 4)(x + 10) = (x)2 + (4 + 10)x + 4 × 10
= x2 +14x + 40

Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

प्रश्न 3.
(x + 8)(x – 10)का मान ज्ञात कीजिए। [NCERT]
हलः
(x + 8)(x -10) = x2 + (8-10)x – 8 × 10
= x2 – 2x – 80

प्रश्न 4.
(3x + 4)(3x – 5) का मान ज्ञात कीजिए। [NCERT]
हलः
(3x + 4)(3x – 5) = (3x)2 + (4 – 5)3x – 4 × 5
= 9x2 – 3x – 20

Ex 4.1 Algebraic Identities लघु उत्तरीय प्रश्न – I (Short Answer Type Questions – I)

प्रश्न 5.
निम्न के मान ज्ञात कीजिए।
(i) (4x – [latex]\frac{1}{2 x}[/latex])2
(ii) (5x2 – 7y2)2
(iii) (x – 0.1)(x + 0.1)
हलः
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

प्रश्न 6.
सर्वसमिकाओं का प्रयोग कर गुणनफल ज्ञात कीजिए। .
(i) 111 × 102
(ii) 105 × 97
(iii) 85 × 96
(iv) 1008 × 995
(v) 991 × 982
(vi) (0.98)2
हलः
(i) 111 × 102 = (100 + 11) × (100 + 2)
= (100)2 + (11 + 2) × 100 + 11 × 2
= 10000 + 1300 + 22 = 11322

(ii) 105 × 97 = (100 + 5) × (100 -3)
= (100)2 + (5 – 3) × 100 – 5 × 3
= 10000 + 200 – 15 = 10185

(iii) 85 × 96 = (100 – 15) × (100 – 4)
= (100)2 + (-15 – 4) × 100 + 15 × 4
= 10000 – 1900 + 60 = 8160

(iv) 10008 × 995 = (1000 + 8) × (1000 – 5)
= (1000)2 + (8 – 5) × 1000 – 8 × 5
= 1000000 + 3000 – 40 = 1002960

(v) 991 × 982 = (1000 – 9) × (1000 – 18)
= (1000) – (9 + 18) × 1000 + 9 × 18
= 1000000 – 27000 + 162 = 973162

(vi) (0.98)2 = (1 – 0.02)2
= (1)2 – 2 × 1 × 0.02 + (0.02)2
= 1 – 0.04 + 0.0004 =0.9604

Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

प्रश्न 7.
सर्वसमिकाओं का प्रयोग कर सरल कीजिए।
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1
हल:
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1
(ii) 185 × 185 – 115 × 115
माना 185 = a तथा 115 = b
a × a – b × b
=a2 – b2 = (a + b)(a – b)
= (185 + 115)(185-115) = (300)(70) = 21000

(iii) 322 × 322 – 2 × 322 × 22 + 22 × 22
माना 322 = a तथा 22 = b
a × a – 2 × a × b + b× b
=a2 – 2ab + b2
= (a – b)2 = (322 – 22)2 = (300)2 = 90000

प्रश्न 8.
यदि [latex]x-\frac{1}{x}=6[/latex], तब [latex]x^{4}+\frac{1}{x^{4}}[/latex] का मान ज्ञात कीजिए।
हलः
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

Ex 4.1 Algebraic Identities लघु उत्तरीय प्रश्न – II (Short Answer Type Questions – II)

प्रश्न 9.
यदि [latex]x+\frac{1}{x}=\sqrt{8}[/latex], तब निम्न के मान ज्ञात कीजिए।
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1 Q 6
हल:
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

प्रश्न 10.
यदि [latex]x-\frac{1}{x}=3[/latex], तब निम्न के मान ज्ञात कीजिए।
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1 Q 8
हल:
(i) [latex]x-\frac{1}{x}=3[/latex]
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

प्रश्न 11
यदि x2 + [latex]\frac{1}{x^{2}}[/latex] = 27, तब निम्न के मान ज्ञात कीजिए।
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1 Q 10
हल:
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

प्रश्न 12.
यदि x = 5 और y = 7 तब 49x2 – 70xy + 25y2 का मान ज्ञात कीजिए।
हल:
x = 5 तथा y = 7
49x2 – 70xy + 25y2 = (7x)2 – 2 × 7x × 5y + (5y)2
= (7x – 5y)2 = (7 × 5 – 5 × 7)2
= (35 – 35)2 = 0

Ex 4.1 Algebraic Identities दीर्घ उत्तरीय प्रश्न (Long Answer Type Questions)

प्रश्न 13.
यदि x = 15 व y = 27 तब 81x2 – 90xy + 25y2 का मान ज्ञात कीजिए।
हलः
81x2 – 90xy + 25y2 = (9x)2 – 2 × 9x × 5y + (5y)2
= (9x – 5y)2 = (9 × 15 – 5 × 27)2
= (135 – 135) = 0

प्रश्न 14.
यदि x + y = 12 व xy = 32 , तब x2 + y2 का मान ज्ञात कीजिए।
हल:
x + y = 12 ………………….. (1)
xy = 32 ……………… (2)
समी० (1) का वर्ग करने पर
x2 + y2 + 2xy = 144
x2 + y2 + 2 × 32 = 144
x2 + y2 = 144 – 64 = 80

प्रश्न 15.
निम्न को सरल कीजिए।
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1
हलः
Balaji Class 9 Maths Solutions Chapter 4 Algebraic Identities Ex 4.1

Balaji Publications Mathematics Class 9 Solutions

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