Question

3. नीचे दिए गए व्यंजक को सरल करें एवं इसका भान ज्ञात करें, जबकि x =2 हो।
4x³ - [9x²- {- 5x³-(2-7x²)+ 6x }]
(1) 12 (2) -12 (3) 14 (4) -14
(नेतरहाट परीक्षा, 1996)​

Answer 1

Answer:

$\sf\small\underline\blue{Correct\:Question:-}$

नीचे दिए गए व्यंजक को सरल करें एवं इसका मान ज्ञात करें, जबकि x =2 हो।

$\longmapsto \:4 {x}^{2} - \big[9 {x}^{2} - \big \{ - 5 {x}^{3} - (2 - 7 {x}^{2} ) + 6x\big \}\big]$

Explanation:

$\sf\small\underline\blue{Given:-}$

• 4x³ - [9x²- {- 5x³-(2-7x²)+ 6x }]

$\small\sf \underline\blue{To\:Find :-}$

• The value of x , if x = 2

$\sf\small\underline\blue{Solution:-}$

Simplifying:

$\Longrightarrow \: 4 {x}^{2} - \big[9 {x}^{2} - \big \{ - 5 {x}^{3} - (2 - 7 {x}^{2} ) + 6x\big \}\big] \\ \\ \Longrightarrow \: 4 {x}^{2} - \big[9 {x}^{2} - \big \{ - 5 {x}^{3} - 2 + 7 {x}^{2} + 6x\big \} \big] \\ \\ \Longrightarrow \: 4 {x}^{3} - \big[9 {x}^{2} - \big \{ - 5 {x}^{3} + 7 {x}^{2} + 6x - 2\big \} \big] \\ \\ </p><p>\Longrightarrow \: 4 {x}^{3} - \big[9 {x}^{2} + 5 {x}^{3} - 7 {x}^{2} - 6x + 2\big] \\ \\ \Longrightarrow \: 4 {x}^{3} - \big[5 {x}^{3} + 2 {x}^{2} - 6x + 2\big] \\ \\ \Longrightarrow \: 4 {x}^{3} - 5 {x}^{3} - 2 {x}^{2} + 6x - 2 \\ \\ \Longrightarrow \: - {x}^{3} - 2 {x}^{2} + 6x - 2$

Now putting the value of x :

$\Longrightarrow \: - {x}^{3} - 2 {x}^{2} + 6x - 2 \\ \\ \Longrightarrow \: - ( - 2)^{3} - 2( - 2)^{2} + 6( - 2) - 2 \\ \\ \Longrightarrow \: 8 - 8 - 12 - 2 = - 14$

Hence ,

The value of x is -14, Option (4) is correct