Question

If ${\sf{x^2 - {\sqrt{7}} x - 1}}$ = 0, then

♦ Find

${\sf{x^{10} - 78x^6 - 79x^2}}$ = ?​

Answer 1

||✪✪ QUESTION ✪✪||

If x² - √7x - 1 = 0, Then Find x¹⁰ - 78x⁶ - 79x² = ?

|| ✰✰ ANSWER ✰✰ ||

➼ x² - √7x - 1 = 0

Taking x common,

➼ x(x - √7 - 1/x) = 0

➼ (x - 1/x) = √7

Squaring both sides and using (a - b)² = a² + b² - 2ab in LHS, we get,

➼ x² + 1/x² - 2 * x * 1/x = 7

➼ (x² + 1/x²) = 9 ------------- Equation ❶

Also, Taking LCM of Equation ❶ in LHS, we get,

➼ (x⁴ + 1)/x² = 9

➼ (x⁴ + 1) = 9x² -------------- Equation ❷

Also, Squaring both sides of Equation ❶ again, we get,

➻ (x² + 1/x²)² = 9²

➻ x⁴ + 1/x⁴ + 2*x²*1/x² = 81

➻ (x⁴ + 1/x⁴) = 79

➻ (x⁴ - 79) = (-1/x⁴) --------------- Equation ❸

________________________

Now, we have to Find :-

☛ x¹⁰ - 78x⁶ - 79x²

☛ x¹⁰ + x⁶ - 79x⁶ - 79x²

☛ x⁶(x⁴ + 1) -79x²(x⁴ + 1)

☛ (x⁴ + 1)(x⁶ - 79x²)

☛ (x⁴ + 1) * x²(x⁴ - 79)

Putting values From Equation ❷ & ❸ now, we get,

☛ (9x²) * x² * (-1/x⁴)

☛ (-9x⁴) * (1/x⁴)

☛ (-9) (Ans.)

Hence, The value of (x¹⁰ - 78x⁶ - 79x²) will be (-9).

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☙❦⟪ Now, For One More Solution Refer To The image ..⟫❦☙

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Answer 2

$\Large\underline{\underline{\sf{Question}:}}$

$\bf \: if \: \green{\sf \: x^2 - {\sqrt{7}}x - 1=0}$

$\red{\bf \: find : x^{10} - 78x^6 - 79x^2} \:$

$\huge\star{\underline{\tt{\red{Answer}}}}\star$ :-

$\underline{\textbf{ \red{Refer} \blue{To} \orange{image} \pink{First}.}} \:$

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$\bigstar \large{\underline{\red{\mathbb{HOPE}\:\color{lime}{ \bf{IT'S}}\:\color{fuchsia}{\mathbb{HELP}}\:\color{aqua}{\bf{You.}}}}}\bigstar$

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