Question

ᴀɴsᴡᴇʀ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ᴡɪᴛʜ ғᴜʟʟ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ
sᴘᴀᴍ ᴡɪʟʟ ʙᴇ ʀᴇᴘᴏʀᴛᴇᴅ
ᴅᴏɴ'ᴛ ᴄᴏᴘʏ ғʀᴏᴍ ɢᴏᴏɢʟᴇ
ɢɪᴠᴇ ᴛʜɴx = ᴛᴀᴋᴇ ᴛʜɴx​

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the Concept of Factorisation method has been used . We see we are given the equation and we can solve this using two methods . For each method we need to take terms common and then find the answer . These common terms will give use roots of the equations .

Let's do it !!

____________________________________________

★ Solution :-

Given,

✒ m⁴ - 256 = 0

We already discussed the two methods to solve this question . Please refer to both methods though both gives same answer .

____________________________________________

~ Simplifying by finding all the roots :-

We see that,

$\\\;\sf{\pink{:\rightarrow\;\;m^{4}\;-\;256\;=\;\bf{0}}}$

• Then, 16 × 16 = 256

$\\\;\sf{:\Longrightarrow\;\;(m^{2}\:\times\:\green{m^{2}})\;-\;(16\:\times\:\green{16})\;=\;\bf{0}}$

$\\\;\sf{:\Longrightarrow\;\;(m^{2})^{\orange{2}}\;-\;(16)^{\orange{2}}\;=\;\bf{0}}$

• By identity, we know that :: (a + b)(a - b) = a² - b²

So,

$\\\;\sf{:\Longrightarrow\;\;\blue{\bigg(m^{2}\;-\;16\bigg) \bigg(m^{2}\;+\;16\bigg)}\;=\;\bf{0}}$

• We know that : 4 × 4 = 16

$\\\;\sf{:\Longrightarrow\;\;\bigg(m^{2}\;-\;(4\:\times\:4)\bigg) \bigg(m^{2}\;+\;16\bigg)\;=\;\bf{0}}$

$\\\;\sf{:\Longrightarrow\;\;\bigg(m^{2}\;-\;(4)^{2}\bigg) \bigg(m^{2}\;+\;16\bigg)\;=\;\bf{0}}$

• Now again using the same identity in first term, we get,

$\\\;\sf{:\Longrightarrow\;\;\bigg( (m\;-\;4)(m\;+\;4)\bigg) \bigg(m^{2}\;+\;16\bigg)\;=\;\bf{0}}$

• Now combing all, we get,

$\\\;\bf{\red{:\Longrightarrow\;\;(m\;-\;4)(m\;+\;4)(m^{2}\;+\;16)\;=\;\bf{0}}}$

This is the required Factorisation . Let's now find the roots of the equation .

• Here either (m - 4) = 0, (m + 4) = 0 or (m² + 16) = 0. Then,

✒ m = 4

✒ m = -4

✒ m² = -16 => m = √-16 = 4i where i is √(-1)

So,

$\\\;\bf{\mapsto\;\;m\;=\;\purple{4,\;-4,\;4i}}$

This is the required answer .

$\\\;\underline{\boxed{\tt{Hence,\;\:m\;=\;\bf{\purple{4,\;-4,\;4i}}}}}$

____________________________________________

★ More to know :-

• Alternative method to solve this question ::

We see we are given,

✒ m⁴ - 256 = 0

This can be written as,

$\\\;\tt{\Longrightarrow\;\;m^{4}\;+\;4m^{3}\;+\;16m^{2}\;+\;64x\;-\;4m^{3}\;-\;16m^{2}\;-\;64x\;-\;256\;=\;0}$

• Now taking the terms common, we get

$\\\;\tt{\Longrightarrow\;\;m(m^{3}\;+\;4m^{2}\;+\;16m\;+\;64)\;-\;4(m^{3}\;+\;4m^{2}\;+\;16m\;+\;64)\;=\;0}$

$\\\;\tt{\Longrightarrow\;\;(m\;-\;4)\:(m^{3}\;+\;4m^{2}\;+\;16m\;+\;64)\;=\;0}$

$\\\;\tt{\Longrightarrow\;\;(m\;-\;4)\:\bigg(m^{2}(m\;+\;4)\;+\;16(m\;+\;4)\bigg)\;=\;0}$

$\\\;\tt{\Longrightarrow\;\;(m\;-\;4)\:(m^{2}+\;16)(m\;+\;4)\;=\;0}$

• This gives us equation like above . Thus both the answers are correct and applicable .

$\\\;\bf{\mapsto\;\;m\;=\;4,\;-4,\;4i}$

Answer 2

Answer:

oii i wanna talk with u, snap ayegi kya? kab?

Step-by-step explanation:

report it after reading it...reply bhi kardooo