Question

if x+y=4 and x.y = 5 find value of x^3 +y^3​

Answer 1

Given (x+y) = 4 ----------(1) , x.y = 5 ------(2)

cubing eq(1) on both sides ,

=> (x+y)^3 = (4)^3

{ (a+b)^3 = a^3+b^3 + 3ab(a+b) }

=> x^3 + y^3 + 3xy(x+y) = 64

=> x^3 + y^3 + 3(5)(4) = 64 {∵ from eq(1)&eq(2) }

=> x^3 + y^3 + 60 = 64

=> x^3 + y^3 = 4

Answer 2

$\bf{\underline{\underline{Question}}}$

$\</strong><strong>s</strong><strong>f</strong><strong>{</strong><strong>IF\</strong><strong>:</strong><strong>x</strong><strong>+</strong><strong>y\</strong><strong>:</strong><strong>=</strong><strong>\</strong><strong>:</strong><strong>4</strong><strong>\</strong><strong>:</strong><strong>and\</strong><strong>:</strong><strong> </strong><strong>xy\</strong><strong>:</strong><strong>=</strong><strong>\</strong><strong>:</strong><strong>5</strong><strong>}</strong><strong>\</strong><strong>\</strong><strong>{</strong><strong>\</strong><strong>s</strong><strong>f</strong><strong>{</strong><strong>T</strong><strong>hen</strong><strong>\</strong><strong>:</strong><strong>Find</strong><strong>\:</strong><strong>the</strong><strong>\:</strong><strong>\</strong><strong>:</strong><strong>value\</strong><strong>:</strong><strong>of</strong><strong>(x^{3}\:+\:y^{3})}</strong><strong>}</strong><strong>$

$\bf{\underline{\underline{</strong><strong>Solution</strong><strong>}}}$

$\bf{</strong><strong>Using</strong><strong>\</strong><strong>:</strong><strong>Formula\</strong><strong>:</strong><strong>(</strong><strong>x^</strong><strong>{</strong><strong>3</strong><strong>}</strong><strong>\</strong><strong>:</strong><strong>+</strong><strong>\</strong><strong>:</strong><strong>y^</strong><strong>{</strong><strong>3</strong><strong>}</strong><strong>)</strong><strong>}$

$\bf{(x^{3}\:+\:y^{3}</strong><strong>)</strong><strong>\</strong><strong>:</strong><strong>=</strong><strong>\</strong><strong>:</strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>y</strong><strong>)</strong><strong>^</strong><strong>{</strong><strong>3</strong><strong>}</strong><strong>-3xy</strong><strong>(</strong><strong>x\</strong><strong>:</strong><strong>+</strong><strong>\</strong><strong>:</strong><strong>y</strong><strong>)</strong><strong>}</strong><strong>$

$\bf{</strong><strong>Putting</strong><strong>\:</strong><strong> Values</strong><strong>,</strong><strong>}$

$\bf{(x^{3}\:+\:y^{3}</strong><strong>)</strong><strong>\:=\:(</strong><strong>4</strong><strong>)^{3}</strong><strong> </strong><strong>-3</strong><strong>(</strong><strong>5</strong><strong>)</strong><strong>(</strong><strong>4</strong><strong>)</strong><strong>}$

$\bf{(x^{3}\:+\:y^{3}</strong><strong>)</strong><strong>\:=\:</strong><strong>6</strong><strong>4</strong><strong>-</strong><strong>6</strong><strong>0</strong><strong>}$

$\bf</strong><strong>{(x^{3}\:+\:y^{3}</strong><strong>)</strong><strong>\:=\:</strong><strong>4</strong><strong>}</strong><strong>$

$\bf{\underline{\underline{</strong><strong>Thanks</strong><strong>}}}$