If a + b + c = 0 , then prove that ( a + b - c ) 2 = 4 a b .

Given that, a + b + c = 0 Now, a + b = - c ⇒ a + b 2 = - c 2 [Squaring both sides] ⇒ a 2 + b 2 + 2 a × b = c ⇒ a + b + 2 a b = c ⇒ a + b - c = - 2 a b ⇒ a + b - c 2 = - 2 a b 2 [Squaring both sides] ⇒ a + b - c 2 = 4 a b Hence, proved.

E M B I B E

All in One Mathematics>Chapter 23 - Sample Question Paper 5 Mathematics>PART A>Q 13

EASY

9th CBSE

IMPORTANT

Earn 100

The radius of a sphere is $3 r$ , then find its volume.

Important Questions on Sample Question Paper 5 Mathematics

EASY

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 23 - Sample Question Paper 5 Mathematics>PART A>Q 14

Find the class mark of the class

60 - 90

.

EASY

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 23 - Sample Question Paper 5 Mathematics>PART A>Q 15

Verify that whether $- 2$ and $3$ are zeroes of the polynomial $x^{2} - x - 6$ .

EASY

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 23 - Sample Question Paper 5 Mathematics>PART A>Q 16

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter Roshni paid

₹ 35

for a book kept for seven days. Write a linear equation which satisfies this data.

EASY

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 23 - Sample Question Paper 5 Mathematics>PART B>Q 21

If

f (x) = x - 7

, find the value of

f (x) - f (- x)

.

EASY

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 23 - Sample Question Paper 5 Mathematics>PART B>Q 21

If

p (x) = 4 x^{5} - 3 x^{4} - 5 x^{3} + x^{2} - 8

, then find

p (- 2)

.

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 23 - Sample Question Paper 5 Mathematics>PART B>Q 21

If

\sqrt{a} + \sqrt{b} + \sqrt{c} = 0

, then prove that

(a + b - c)^{2} = 4 a b

.

HARD

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 23 - Sample Question Paper 5 Mathematics>PART B>Q 22

A class teacher gave students coloured papers made by recycling of waste products in shape of quadrilateral. She asked them to make a parallelogram from it using paper folding. Then, prove that it is a parallelogram.

Question Image