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RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

February 20, 2019 by Fazal Leave a Comment

RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5 is part of RBSE Solutions for Class 9 Maths. Here we have given Rajasthan Board RBSE Class 9 Maths Chapter 3 बहुपद Exercise 3.5.

Board RBSE
Textbook SIERT, Rajasthan
Class Class 9
Subject Maths
Chapter Chapter 3
Chapter Name बहुपद
Exercise Exercise 3.5
Number of Questions Solved 12
Category RBSE Solutions

Rajasthan Board RBSE Class 9 Maths Chapter 3 बहुपद Ex 3.5

प्रश्न 1.
उपयुक्त सर्वसमिकाओं का प्रयोग करके गुणनफल ज्ञात कीजिए।
(i) (x + 3) (x + 7)
(ii) (x – 5) (x + 8)
(iii) (2x + 7) (3x – 5)
(iv) (5 – 3x) (3 + 2x)
(v) (x2 + \(\frac { 3 }{ 5 }\)) (x2 – \(\frac { 3 }{ 5 }\))
(vi) (x + 2) (x – 5)
हल:
(x + a) (x + b) = x2 + (a + b) x+ ab से
(i) (x + 3) (x + 7) = x + 10x + 21
(ii) (x – 5) (x + 8) = {x + (-5)} (x + 8)
= x2 + (-5 + 8) x + (-5) x 8
= x2 + 3x – 40
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 2.
बीजीय सर्वसमिकाओं का प्रयोग करके गुणनफल ज्ञात कीजिए।
(i) 104 x 109
(ii) 94 x 97
(iii) 103 x 97
हल:
(i) 104 x 109 = (100 + 4) (100 + 9) = (100)2 + (4 + 9) 100 + 4 x 9 = 11336
(ii) 94 x 97
= (100 – 6) (100 – 3)
= [100 + (-6)] [100 + (-3)]
= (100)2 + (-6 – 3) 100+ (-6) x (-3)
= 10000 – 900 + 18
= 9118
(iii) 103 x 97
= (100 + 3) (100 – 3)
= (100)2 – (3)2
= 10000 – 9
= 9991

RBSE Solutions

प्रश्न 3.
उपयुक्त सर्वसमिकाओं का प्रयोग करके गुणनखण्ड कीजिए।
(i) x2 + 6xy + 9y
(ii) x2 – 4x + 4
(ii) \(\frac { { x }^{ 2 } }{ 100 } -{ y }^{ 2 }\)
हल:
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 4.
उपयुक्त सर्वसमिका का प्रयोग करके निम्नलिखित का विस्तार कीजिए।
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5
हल:
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 5.
गुणनखण्ड कीजिए-
(i) 9x2 + 4y2 + 16z2 – 12xy – 16yz + 24xz
(ii) x2 +2y2 + 8z2 + 2√2 xy – 8yz – 4√2xz
हल:
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 6.
निम्न घनों का विस्तार कीजिए-
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5
हल:
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 7.
उपयुक्त सर्वसमिकाओं का प्रयोग करके माने ज्ञात कीजिए-
(i) (98)3
(ii) (103)3
(iii) (999)3
हल:
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 8.
गुणनखण्ड कीजिए
(i) x3 + 8y3 + 6x2y + 12xy2
(ii) 27a3 – 8b3 – 54a2b + 36ab2
(iii) 27 – 125x3 – 135x + 225x2
(iv) 125x3 – 64y3 – 300x2y + 240xy2
हल:
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 9.
गुणनखण्ड कीजिए
(i) 64a3 + 27b3
(ii) 125x3 – 8y3
हल:
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 10.
सत्यापित कीजिए-
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5
हल
RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5

RBSE Solutions

प्रश्न 11.
यदि x + y + z = 0 हो तो सत्यापित कीजिए कि x3 + y3 + z3 = 3xyz
हल:
दिया है, x + y + z = 0 ⇒ x + y = -z
दोनों पक्षों का घन करने पर,
(x + y)3 = (-z)3
⇒ x3 + y3 + 3xy (x + y) = -z3
⇒ x3 + y3 + 3xy(-z) = -z3 (∵ x + y = -z)
⇒ x3 + y3 + z3 = 3xyz
इति सिद्धम्

RBSE Solutions

प्रश्न 12.
उपयुक्त बीजीय सर्वसमिका का प्रयोग करते हुए गणना कीजिए-
(i) (30)3 + (20)3 + (-50)3
(ii) (-15)3 + (28)3 + (-13)3
[संकेत : सर्वसमिका का प्रयोग करें, यदि x + y + z = 0 हो तो x3 + y3 + z3 = 3xyz]
हल:
(i) 30 + 20 – 50 = 0
यदि x + y + z = 0 है तो x3 + y3 + z3 = 3xyz से
(30)3 + (20)3 + (-50)3
= 3 x 30 x 20 x (50)
= 1800 x (-50)
= -90000
(ii) -15 + 28 – 13 = 0
यदि x + y + z = 0 है तो x3 + y3 + z3 = 3xyz से
(-15)3 + (28)3 + (-13)3
= 3 x (-15) x 28 x (-13)
= -45 x 28 x (-13)
= -1260 x -13
= 16380

RBSE Solutions

We hope the given RBSE Solutions for Class 9 Maths Chapter 3 बहुपद Ex 3.5 will help you. If you have any query regarding Rajasthan Board RBSE Class 9 Maths Chapter 3 बहुपद Exercise 3.5, drop a comment below and we will get back to you at the earliest.

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