C-05-Q045mediumsingle_mcqIf (5+1)x+4=45(\sqrt{5} + 1)x + 4 = 4\sqrt{5}(5+1)x+4=45, then xxx equals—a6−256 - 2\sqrt{5}6−25b4−254 - 2\sqrt{5}4−25c5−1\sqrt{5} - 15−1d25−42\sqrt{5} - 425−4ব্যাখ্যাIsolating gives (5+1)x=45−4=4(5−1)(\sqrt5+1)x=4\sqrt5-4=4(\sqrt5-1)(5+1)x=45−4=4(5−1), so x=4(5−1)5+1x=\dfrac{4(\sqrt5-1)}{\sqrt5+1}x=5+14(5−1). Rationalizing by (5−1)(\sqrt5-1)(5−1) yields x=4(5−1)24=6−25x=\dfrac{4(\sqrt5-1)^2}{4}=6-2\sqrt5x=44(5−1)2=6−25.