Question

$\bf \: x = 2 + \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2} } } } } ...$
Find out x ​

Answer 1

${\maltese \; \; {\underline{\purple{\underline{\pmb{\bf{Given : }}}}}}}$

$\qquad \qquad {\bigstar\; {\underline{\boxed{\tt{ x = 2+ \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2 .... \infty} } } } }}}}}$

${\maltese \; \; {\underline{\purple{\underline{\pmb{\bf{To \; Find : }}}}}}}$

• The value of the variable which is denoted with the sign x

${\maltese \; \; {\underline{\purple{\underline{\pmb{\bf{ Required \; Solution: }}}}}}}$

• The value of x should be four to satisfy the condition

${\maltese \; \; {\underline{\purple{\underline{\pmb{\bf{Full \; Solution : }}}}}}}$

➤ Here we observe that x - 2 equals to $\bf \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2 ... \infty} }} }$ so , we can rewrite the equation as such that ,

$\longrightarrow \sf x - 2 = \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2 ...\infty} } } } \\ \\ \\ \longrightarrow \sf x - 2 = \sqrt{2 + x - 2} \\ \\ \\ \longrightarrow \sf x - 2 = \sqrt{x} \\ \\ \\ \qquad \qquad {\purple{\underline{\mathbb{ SQUARING \; ON \; BOTH \; SIDES }}}}$

$\longrightarrow \sf x^2 - 4x + 4 = x \\ \\ \\ \longrightarrow \sf x^2 - 5x + 4 = 0 \\ \\ \\ \qquad {\purple{\underline{\mathbb{ FACTORISING \; THE \; EQUATION}}}}$

$\longrightarrow \sf x^{2} - 5x + 4 = 0 \\ \\ \\ \longrightarrow \sf x^{2} - 4x - 1x + 4 = 0 \\ \\ \\ \longrightarrow \sf x( x - 4 ) - 1 ( x - 4 ) = 0 \\ \\ \\ \longrightarrow \sf ( x - 1 ) ( x - 4 ) \\ \\ \\ \qquad \qquad {\purple{\underline{\mathbb{ FINDING \; THE \; ROOTS}}}}$

$\longrightarrow \sf x - 1 = 0 \\ \\ \longrightarrow {\red{\boxed{\frak{ x = 1}}}} \\ \\ \\ \longrightarrow \sf x - 4 = 0 \\ \\ \longrightarrow {\red{\boxed{\frak{ x = 4}}}}$

${\maltese \; \; {\underline{\purple{\underline{\pmb{\bf{Since \; we \; observe: }}}}}}}$

• That it is give that x equals to 2 + root of 2 and so on so the value of x will be in thee terms more than that of the term 2 and as we've figured out that the roots are 1 , 4 so the value of x will be 4 as 4 > 2 whereas 1 < 2

${\maltese \; \; {\underline{\purple{\underline{\pmb{\bf{Therfore : }}}}}}}$

• The value of x in the equation is 4

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Answer 2

Step-by-step explanation:

Ohm's Law is a formula used to calculate the relationship between voltage, current and resistance in an electrical circuit. To students of electronics, Ohm's Law (E = IR) is as fundamentally important as Einstein's Relativity equation (E = mc²) is to physicists. E = I x R.